第六章 濕空氣學 · web view國立台北科技大學 書報討論心得報告 報告題目:...
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第六章 濕空氣學
國立台北科技大學
書報討論心得報告
報告題目:
濕空氣學
PSYCHROMETRICS
（2001 ASHRAE HANDBOOK –FUNDAMENTALS CHAPTER 6）
目 錄
2乾空氣及濕空氣的構成
美國標準大氣空氣2
溼空氣之熱力性質3
水在飽和狀態之熱力性質8
濕度的參數13
涉及飽和的濕度參數13
乾空氣及濕空氣的理想氣體關係式14
熱力溼球溫度和露點溫度16
溼空氣性質的數值計算17
WS及ψ精確關係之計算18
用於標準壓力之濕空氣性質表19
典型空氣調節過程21
濕空氣之（熱、質）傳性質28
空氣、水及蒸汽性質30
符號31
參考文獻33
濕空氣學
濕空氣學論及溼空氣的熱力學性質和利用這些性質來分析涉及溼空氣的狀況和過程(方法)。Hyland 和 Wexler(1983a,1983b)為溼空氣和水的熱力學性質發展了公式。能夠把理想氣體關係用於多數空氣調節問題而取代這些公式。Threlkeld( 1970 ) 發表在標準的大氣壓力下溫度範圍在- 50到50℃時，計算標準空氣之溼度比、焓、和比容，其誤差是不到0.7%。此外，誤差會隨著壓力增加而減少。
本章節討論理想氣體關係和描述他它們用於一般空氣調節的問題。 這些公式是由Hyland 和Wexler ( 1983a )發展出來的，在需要更精確也可以被使用。
乾空氣及濕空氣的構成
大氣中的空氣含有許多氣體成份以及水的蒸汽和各式各樣的污染物質（像是煙、花粉、及氣體等污染物不正常地出現在遠離污染源的自由空氣中）。
當把所有水蒸汽和污染物質都從大氣空氣移走時，就是乾空氣。乾空氣的構成的成份是相對地固定，但是因時間、地理位置、及海拔高度等因素，某些成份比例會發生些微的變化。Harrison (1965)
基於體積把乾空氣的近似百分比成份列成表: 氮–78.084 ； 氧氣–20.9476 ； 氬–0.934 ； 二氧化碳–0.0314 ；氖–0.001818 ；氦–0.000524 ； 甲烷– 0.00015 ； 硫二氧化物–0 到 0.0001 ； 氫–0.00005 ； 和如氪、氙、和臭氧等較少的成份–0.0002 。所有部分的相關分子量， 因為乾(燥)的空氣是 28.9645，基於碳-12尺標（scale) ( Harrison 1965 )。 基於碳- 12 尺標（scale) ，乾空氣的氣體常數是：
Ra = 8314.41/28.9645 = 287.055 J/(kg．k) ( 1 )
溼空氣是乾空氣和水蒸汽的一雙 (或者兩種成份) 混合物。溼空氣中水蒸汽的含量從零 (乾空氣) 到最大量變化是取決於於溫度和壓力。後面的條件與飽和有關， 在溼空氣和凝結水相(液體或者固體) 之間維持平衡的狀態。除非是如下陳述， 飽和涉及溼空氣和凝結相之間的均一（flat）界面表面。水的分子量在碳-12尺標（scale)上是18.012628。 基於碳- 12 尺標（scale) ，水蒸汽的氣體常數是：
Rw= 8314.41/18.01528 = 461.520 J/( kg．k) ( 2 )
美國標準大氣空氣
大氣中空氣的溫度和大氣壓力會隨著當地地理高度以及氣象條件改變。標準的大氣是為了估算各種高度之空氣性質提供參考的一個標準。在海平面上，標準的溫度是 15 ℃； 標準的大氣壓力是 101.325kPa。溫度假設為隨著經過對流層（較低的氣壓）的高度增加而線性地減少，和以在同溫層較低（空氣可到達）的範圍中是不變的。較低的大氣被假設由相當於理想氣體的乾空氣所組成。 重力也是標準的固定值–9.806 65 m/s2。表1是高度10000公尺以下為概述性質資料。
表1 中之數值可以由下列方程式計算
p＝101.325(1－2.5577×10-5 Z)5.2559 ( 3 )
表 1 從海平面到10km 高度之標準空氣資料
海拔高度, m溫度, ℃壓力, kPa
-50018.2107.478
015.0101.325
50011.895.461
10008.589.875
15005.284.556
20002.079.495
2500-1.274.682
3000-4.570.108
4000-11.061.640
5000-17.554.020
6000-24.047.181
7000-30.541.061
8000-37.035.600
9000-43.530.742
10000-5026.436
12000 -6319.284
14000-7613.786
16000-899.632
18000-1026.556
20000-1154.328
資料源自於國家航空暨太空總署(NASA) (1976)
以溫度為高度函數之方程式是寫成:
t =15－0.0065×Z ( 4 )
其中 Z = 高度,m
P = 大氣壓力,kPa
t = 溫度, K
方程式 ( 3 ) 和 ( 4 ) 從 -5000m到 11000 m是精確的，在更高高度之標準大氣的氣壓及其他廣泛的物理性質表格能夠在國家航空暨太空總署中被找到 ( 1976美國標準大氣) 。
溼空氣之熱力性質
表2是Hyland 和 Wexler (1983a，1983b ) 從公式發展而來，是基於熱力學溫度尺標展現熱力學性質的數值。這個理想尺標與從用作物質測量的實際溫度尺標稍微地不同。 例如， 水的標準的沸點(在 101.325 kPa) 在這個尺標上是99.97℃而非是傳統的100℃。目前多數測量基於1990年的國際實用溫度尺標（IPTS-90）。下面是簡單地描述表2的每一欄位。
t =攝氏溫度，基於熱力學溫度尺標與開氏溫度(K)的絕對溫度T相關和由關係:
T = t + 273.15
ws =飽和狀態的溼度比，氣相(溼空氣)在平衡中有凝結相(液體或者固體)存在，在既定的溫度和壓力(標準的大氣壓力)的條件。處於既定的溫度和壓力狀態，溼度比W能夠從零到Ws。
va=乾空氣的比容， m3 /kg。
vas= vs – va ，在相同壓力及溫度下，每公斤乾空氣在飽和濕空氣之體積和乾空氣在空氣本身之比容(m3 /kg of dry air)差值。
vs = 每公斤乾空氣在飽和濕空氣之體積，m3/kg of dry air。
ha = 乾空氣之比焓， kJ/kg of dry air。表2中，乾空氣的比焓在0℃及標準大氣壓下被指定為0。
has = h s- ha ，在相同壓力及溫度下，每公斤乾空氣在飽和濕空氣之焓和乾空氣在空氣本身之比容(kJ /kg of dry air)差值。
hs =每公斤乾空氣在飽和濕空氣之焓， kJ/kg of dry air.
hw=在既定的溫度和壓力下，飽和空氣在平衡中之凝結水(液體或者固體)比焓， kJ/kg of water。液態水的比焓在三相點（0.01℃）及飽和壓力下被指定為0。
註釋， hw比蒸汽表中飽和純凝結相的焓值大，是因為壓力由飽和壓力增加到 101.325 kPa，加上空氣存在影響。
Sa =乾空氣之比熵，kJ/(kg．K). 表2中，乾空氣的比熵在0℃及標準大氣壓下被指定為0。
sas =ss-sa ，在相同壓力及溫度下，每公斤乾空氣在飽和濕空氣之熵和乾空氣在空氣本身之比熵(kJ /kg．K)差值。
ss=每公斤乾空氣在飽和濕空氣之熵， kJ/(kg．K)。
sw =飽和空氣在平衡中之凝結水(液體或者固體)比熵， kJ/kg．K。就像hw， sw 與飽和純凝結水的熵值不同。
ps = 在飽和濕空氣下水蒸汽分壓， kPa。壓力ps不同於純水的飽和水蒸汽壓力，在狀況演練時是可忽略地。因此，在方程式中在相同的壓力及溫度下pws 出現時可以用ps代入。壓力ps 被定義為ps = x ws p，其中x ws 是濕空氣在溫度t及壓力p飽和狀態下之水蒸汽的摩爾分數(mole fraction)。而 p是濕空氣之大氣壓力。
表2 濕空氣熱力性質(標準大氣壓力, 101.325 kPa)
冷凝水
濕度蒸汽
溫度比,比容, 比焓,比熵,
比焓比熵, 壓力,
t,kgw/kgda m3/kg (dry air) kJ/kg (dry air) J/(kg．K) (dry air) kJ/kgkJ/(kg．K)kPa 溫度
℃W sv a v as v s h ah ash ss as ass sh w s w p s,℃
-60 0.0000067 0.6027 0.0000 0.6027 -60.351 0.017-60.334 -0.2495 0.0001 -0.2494 -446.29 -1.68540.00108 -60
-59 0.0000076 0.6056 0.0000 0.6056 -59.344 0.018 -59.326 -0.2448 0.0001 -0.2447 -444.63 -1.67760.00124 -59
-58 0.0000087 0.6084 0.0000 0.6084 -58.338 0.021 -58.317 -0.2401 0.0001 -0.2400 -442.95 -1.6698 0.00141 -58
-570.00001000.6113 0.0000 0.6113 -57.332 0.024 -57.308 -0.2354 0.0001 -0.2353 -441.27 -1.6620 0.00161 -57
-560.00001140.61410.00000.6141-56.3260.028-56.298-0.23080.0001-0.2306-439.58-1.65420.00184-56
-550.00001290.61700.00000.6170-55.3190.031-55.288-0.22610.0002-0.2260-437.89-1.64640.00209-55
-540.00001470.61980.00000.6198-54.3130.036-54.278-0.22150.0002-0.2214-436.19-1.63860.00238-54
-530.00001670.62260.00000.6227-53.3070.041-53.267-0.21700.0002-0.2168-434.48-1.63080.00271-53
-520.00001900.62550.00000.6255-52.3010.046-52.255-0.21240.0002-0.2122-432.76-1.62300.00307-52
-510.00002150.62830.00000.6284-51.2950.052-51.243-0.20790.0002-0.2076-431.03-1.61530.00348-51
-500.00002430.63120.00000.6312-50.2890.059-50.230-0.20330.0003-0.2031-429.30-1.60750.00394-50
-490.00002750.63400.00000.6341-49.2830.067-49.216-0.19880.0003-0.1985-427.56-1.59970.00445-49
-480.00003110.63690.00000.6369-48.2770.075-48.202-0.19440.0004-0.1940-425.82-1.59190.00503-48
-470.00003500.63970.00000.6398-47.2710.085-47.186-0.18990.0004-0.1895-424.06-1.58420.00568-47
-460.00003950.64260.00000.6426-46.2650.095-46.170-0.18550.0004-0.1850-422.30-1.57640.00640-46
-450.00004450.64540.00000.6455-45.2590.108-45.151-0.18110.0005-0.1805-420.54-1.56860.00721-45
-440.00005000.64830.00010.6483-44.2530.121-44.132-0.17670.0006-0.1761-418.76-1.56090.00811-44
-430.00005620.65110.00010.6512-43.2470.137-43.111-0.17230.0006-0.1716-416.98-1.55310.00911-43
-420.00006310.65400.00010.6540-42.2410.153-42.088-0.16790.0007-0.1672-415.19-1.54530.01022-42
-410.00007080.65680.00010.6569-41.2350.172-41.063-0.16360.0008-0.1628-413.39-1.53760.01147-41
-400.00007930.65970.00010.6597-40.2290.192-40.037-0.15920.0009-0.1584-411.59-1.52980.01285-40
-390.00008870.66250.00010.6626-39.2240.216-39.007-0.15490.0010-0.1540-409.77-1.52210.01438-39
-380.00009920.66530.00010.6654-38.2180.241-37.976-0.15070.0011-0.1496-407.96-1.51430.01608-38
-370.00011080.66820.00010.6683-37.2120.270-36.942-0.14640.0012-0.1452-406.13-1.50660.01796-37
-360.00012370.67100.00010.6712-36.2060.302-35.905-0.14210.0014-0.1408-404.29-1.49880.02005-36
-350.00013790.67390.00010.6740-35.2000.336-34.864-0.13790.0015-0.1364-402.45-1.49110.02235-35
-340.00015360.67670.00020.6769-34.1950.375-33.820-0.13370.0017-0.1320-400.60-1.48330.02490-34
-330.00017100.67960.00020.6798-33.1890.417-32.772-0.12950.0018-0.1276-398.75-1.47560.02772-33
-320.00019020.68240.00020.6826-32.1830.464-31.718-0.12530.0020-0.1233-396.89-1.46780.03082-32
-310.00021130.68530.00020.6855-31.1780.517-30.661-0.12120.0023-0.1189-395.01-1.46010.03425-31
-300.00023460.68810.00030.6884-30.1710.574-29.597-0.11700.0025-0.1145-393.14-1.45240.03802-30
-290.00026020.69090.00030.6912-29.1660.636-28.529-0.11290.0028-0.1101-391.25-1.44460.04217-29
-280.00028830.69380.00030.6941-28.1600.707-27.454-0.10880.0031-0.1057-389.36-1.43690.04673-28
-270.00031930.69660.00040.6970-27.1540.782-26.372-0.10470.0034-0.1013-387.46-1.42910.05175-27
-260.00035330.69950.00040.6999-26.1490.867-25.282-0.10060.0037-0.0969-385.55-1.42140.05725-26
-250.00039050.70230.00040.7028-25.1430.959-24.184-0.09650.0041-0.0924-383.63-1.41370.06329-25
-240.00043140.70520.00050.7057-24.1371.059-23.078-0.09250.0045-0.0880-381.71-1.40590.06991-24
-230.00047620.70800.00050.7086-23.1321.171-21.961-0.08850.0050-0.0835-379.78-1.39820.07716-23
-220.00052510.71090.00060.7115-22.1261.292-20.834-0.08450.0054-0.0790-377.84-1.39050.08510-22
-210.00057870.71370.00070.7144-21.1201.425-19.695-0.08050.0060-0.0745-375.90-1.38280.09378-21
-200.00063730.71650.00070.7173-20.1151.570-18.545-0.07650.0066-0.0699-373.95-1.37500.10326-20
-190.00070130.71940.00080.7202-19.1091.729-17.380-0.07250.0072-0.0653-371.99-1.36730.11362-19
-180.00077110.72220.00090.7231-18.1031.902-16.201-0.06860.0079-0.0607-370.02-1.35960.12492-18
-170.00084730.72510.00100.7261-17.0982.092-15.006-0.06460.0086-0.0560-368.04-1.35180.13725-17
-160.00093030.72790.00110.7290-16.0922.299-13.793-0.06070.0094-0.0513-366.06-1.34410.15068-16
-150.00102070.73080.00120.7320-15.0862.524-12.562-0.05680.0103-0.0465-364.07-1.33640.16530-15
-140.00111910.73360.00130.7349-14.0802.769-11.311-0.05290.0113-0.0416-362.07-1.32870.18122-14
-130.00122620.73640.00140.7379-13.0753.036-10.039-0.04900.0123-0.0367-360.07-1.32100.19852-13
-120.00134250.73930.00160.7409-12.0693.327-8.742-0.04520.0134-0.0318-358.06-1.31320.21732-12
-110.00146900.74210.00170.7439-11.0633.642-7.421-0.04130.0146-0.0267-356.04-1.30550.23775-11
-100.00160620.74500.00190.7469-10.0573.986-6.072-0.03750.0160-0.0215-354.01-1.29780.25991-10
-90.00175510.74780.00210.7499-9.0524.358-4.693-0.03370.0174-0.0163-351.97-1.29010.28395-9
-80.00191660.75070.00230.7530-8.0464.764-3.283-0.02990.0189-0.0110-349.93-1.28240.30999-8
-70.00209160.75350.00250.7560-7.0405.202-1.838-0.02610.0206-0.0055-347.88-1.27460.33821-7
-60.00228110.75630.00280.7591-6.0355.677-0.357-0.02230.0224-0.0000-345.82-1.26690.36874-6
-50.00248620.75920.00300.7622-5.0296.1921.164-0.01860.0243-0.0057-343.76-1.25920.40178-5
-40.00270810.76200.00330.7653-4.0236.7512.728-0.01480.0264-0.0115-341.69-1.25150.43748-4
-30.00294800.76490.00360.7685-3.0177.3534.336-0.01110.0286-0.0175-339.61-1.24380.47606-3
-20.00320740.76770.00390.7717-2.0118.0075.995-0.00740.0310-0.0236-337.52-1.23610.51773-2
表2 濕空氣熱力性質(標準大氣壓力, 101.325 kPa)(續)
冷凝水
濕度蒸汽
溫度比,比容, 比焓,比熵,
比焓比熵, 壓力,
t,kgw/kgda m3/kg (dry air) kJ/kg (dry air) J/(kg．K) (dry air) kJ/kgkJ/(kg．K)kPa 溫度
℃W sv a v as v s h ah ash ss as ass sh w s w p s,℃
-10.00348740.77050.00430.7749-1.0068.7127.706-0.00370.0336-0.0299-335.42-1.22840.56268-1
00.00378950.77340.00470.7781-0.0009.4739.4730.00000.03640.0364-333.32-1.22060.61117-0
0*0.0037890.77340.00470.7781-0.0009.4739.4730.00000.03640.03640.06-0.00010.61120
10.0040760.77620.00510.78131.00610.19711.2030.00370.03910.04274.280.01530.65711
20.0043810.77910.00550.78452.01210.97012.9820.00730.04190.04928.490.03060.70602
30.0047070.78190.00590.78783.01811.79314.8110.01100.04490.055912.700.04590.75813
40.0050540.78480.00640.79114.02412.67216.6960.01460.04800.062716.910.06110.81354
50.0054240.78760.00680.79445.02913.61018.6390.01820.05140.069721.120.07620.87255
60.0058180.79040.00740.79786.03614.60820.6440.02190.05500.076925.320.09130.93536
70.0062370.79330.00790.80127.04115.67122.7130.02550.05880.084329.520.10641.00207
80.0066830.79610.00850.80468.04716.80524.8520.02900.06280.091933.720.12131.07298
90.0071570.79900.00920.80819.05318.01027.0640.03260.06710.099737.920.13621.14819
100.0076610.80180.00980.811610.05919.29329.3520.03620.07170.107842.110.15111.228010
110.0081970.80460.01060.815211.06520.65831.7240.03970.07650.116246.310.16591.312811
120.0087660.80750.01130.818812.07122.10834.1790.04330.08160.124850.500.18061.402612
130.0093700.81030.01220.822513.07723.64936.7260.04680.08700.133754.690.19531.497913
140.0100120.81320.01310.826214.08425.28639.3700.05030.09270.143058.880.20991.598714
150.0106920.81600.01400.830015.09027.02342.1130.05380.09870.152563.070.22441.705515
160.0114130.81880.01500.833816.09628.86744.9630.05730.10510.162467.260.23891.818516
170.0121780.82170.01600.837717.10230.82447.9260.06070.11190.172671.440.25341.938017
180.0129890.82450.01720.841718.10832.90051.0080.06420.11900.183275.630.26782.064318
190.0138480.82740.01840.845719.11435.10154.2160.06770.12660.194279.810.28212.197919
200.0147580.83020.01960.849820.12137.43457.5550.07110.13460.205784.000.29652.338920
210.0157210.83300.02100.854021.12739.90861.0350.07450.14300.217588.180.31072.487821
220.0167410.83590.02240.858322.13342.52764.6600.07790.15190.229892.360.32492.644822
230.0178210.83870.02400.862723.14045.30168.4400.08130.16130.242696.550.33902.810523
240.0189630.84160.02560.867124.14648.23972.3850.08470.17120.2559100.730.35312.985224
250.0201700.84440.02730.871725.15351.34776.5000.08810.18170.2698104.910.36723.169325
260.0214480.84720.02910.876426.15954.63880.7980.09150.19270.2842109.090.38123.363326
270.0227980.85010.03110.881127.16558.12085.2850.09480.20440.2992113.270.39513.567427
280.0242260.85290.03310.886028.17261.80489.9760.09820.21660.3148117.450.40903.782328
290.0257350.85580.03530.891029.17965.69994.8780.10150.22960.3311121.630.42294.008429
300.0273290.85860.03760.896230.18569.820100.0060.10480.24320.3481125.810.43674.246230
310.0290140.86140.04000.901531.19274.177105.3690.10820.25760.3658129.990.45054.496131
320.0307930.86430.04260.906932.19878.780110.9790.11150.27280.3842134.170.46424.758632
330.0326740.86710.04540.912533.20583.652116.8570.11480.28870.4035138.350.47795.034533
340.0346600.87000.04830.918334.21288.799123.0110.11800.30560.4236142.530.49155.324234
350.0367560.87280.05140.924235.21994.236129.4550.12130.32330.4446146.710.50515.628035
360.0389710.87560.05460.930336.22699.983136.2090.12460.34200.4666150.890.51865.946836
370.0413090.87850.05810.936637.233106.058143.2900.12780.36170.4895155.070.53216.281237
380.0437780.88130.06180.943138.239112.474150.7130.13110.38240.5135159.250.54566.631538
390.0463860.88420.06570.949839.246119.258158.5040.13430.40430.5386163.430.55906.998839
400.0491410.88700.06980.956840.253126.430166.6830.13750.42730.5649167.610.57247.383840
410.0520490.88980.07410.964041.261134.005175.2650.14070.45160.5923171.790.58577.786641
420.0551190.89270.07880.971442.268142.007184.2750.14390.47710.6211175.970.59908.208142
430.0583650.89550.08370.979243.275150.475193.7490.14710.50410.6512180.150.61228.649543
440.0617910.89830.08880.987244.282159.417203.6990.15030.53250.6828184.330.62549.111044
450.0654110.90120.09430.995545.289168.874214.1640.15350.56240.7159188.510.63869.593545
460.0692390.90400.10021.004246.296178.882225.1790.15660.59400.7507192.690.651710.098246
470.0732820.90690.10631.013247.304189.455236.7590.15980.62730.7871196.880.664810.625047
480.0775560.90970.11291.022648.311200.644248.9550.16290.66240.8253201.060.677811.175448
490.0820770.91250.11981.032349.319212.485261.8030.16610.69940.8655205.240.690811.750249
500.0868580.91540.12721.042550.326225.019275.3450.16920.73850.9077209.420.703812.350350
510.0919180.91820.13501.053251.334238.290289.6240.17230.77980.9521213.600.716712.976451
520.0972720.92110.14331.064352.341252.340304.6820.17540.82340.9988217.780.729613.629352
530.1029480.92390.15211.076053.349267.247320.5960.17850.86951.0480221.970.742414.310853
540.1089540.92670.16141.088254.357283.031337.3880.18160.91821.0998226.150.755215.020554
550.1153210.92960.17131.100955.365299.772355.1370.18470.96981.1544230.330.768015.760155
560.1220770.93240.18191.114356.373317.549373.9220.18771.02431.2120234.520.780716.531156
表2 濕空氣熱力性質(標準大氣壓力, 101.325 kPa)(續)
冷凝水
濕度蒸汽
溫度比,比容, 比焓,比熵,
比焓比熵, 壓力,
t,kgw/kgda m3/kg (dry air) kJ/kg (dry air) J/(kg．K) (dry air) kJ/kgkJ/(kg．K)kPa 溫度
℃W sv a v as v s h ah ash ss as ass sh w s w p s,℃
570.1292430.93530.19321.128457.381336.417393.7980.19081.08201.2728238.700.793417.333757
580.1368510.93810.20511.143258.389356.461414.8500.19381.14321.3370242.880.806118.169158
590.1449420.94090.21791.158859.397377.788437.1850.19691.20811.4050247.070.818719.039359
600.153540.94380.23151.175260.405400.458460.8630.19991.27691.4768251.250.831319.943960
610.162690.94660.24601.192661.413424.624486.0360.20291.35001.5530255.440.843820.885861
620.172440.94940.26141.210962.421450.377512.7980.20591.42781.6337259.620.856321.865162
630.182840.95230.27801.230363.429477.837541.2660.20891.51041.7194263.810.868822.882663
640.193930.95510.29571.250864.438507.177571.6150.21191.59851.8105268.000.881223.940564
650.205790.95800.31471.272665.446538.548603.9950.21491.69251.9074272.180.893625.039765
660.218480.96080.33501.295866.455572.116638.5710.21791.79272.0106276.370.906026.181066
670.232070.96360.35681.320467.463608.103675.5660.22091.89992.1208280.560.918327.366467
680.246640.96650.38031.346768.472646.724715.1960.22382.01472.2385284.750.930628.596768
690.262310.96930.40551.374969.481688.261757.7420.22682.13782.3646288.940.942929.874169
700.279160.97210.43281.404970.489732.959803.4480.22972.26992.4996293.130.955131.198670
710.297340.97500.46221.437271.498781.208852.7060.23272.41222.6448297.320.967332.573471
720.316980.97780.49411.471972.507833.335905.8420.23562.56552.8010301.510.979433.998372
730.338240.98070.52871.509373.516889.807963.3230.23852.73112.9696305.700.991635.475973
740.361300.98350.56621.549774.525951.0771025.6030.24142.91043.1518309.891.003737.006374
750.386410.98630.60721.593575.5351017.8411093.3750.24433.10523.3496314.081.015738.594075
760.413770.98920.65191.641176.5431090.6281167.1720.24723.31713.5644318.281.027840.236976
770.443720.99200.70101.693077.5531170.3281247.8810.25013.54863.7987322.471.039841.938877
780.476630.99480.75501.749878.5621257.9211336.4830.25303.80234.0553326.671.051743.702078
790.512840.99770.81451.812179.5721354.3471433.9180.25594.08104.3368330.861.063645.524879
800.552951.00050.88051.881080.5811461.2001541.7810.25874.38904.6477335.061.075547.413580
810.597511.00340.95391.957281.5911579.9611661.5520.26164.73054.9921339.251.087449.367081
820.647241.00621.03602.042282.6001712.5471795.1480.26445.11085.3753343.451.099351.386082
830.703111.00901.12832.137383.6101861.5481945.1580.26735.53725.8045347.651.111153.474683
840.766241.01191.23282.244684.6202029.9832114.6030.27016.01816.2882351.851.122855.633784
850.838121.01471.35182.366685.6302221.8062307.4360.27296.56446.8373356.051.134657.865885
860.920621.01751.48872.506286.6402442.0362528.6770.27577.19017.4658360.251.146360.172786
871.016111.02041.64732.667687.6502697.0162784.6660.27857.91288.1914364.451.158062.554487
881.128001.02321.83332.856588.6612995.8903084.5510.28138.75809.0393368.651.169665.016688
891.260641.02612.05403.080089.6713350.2543439.9250.28419.757710.0419372.861.181267.558189
901.420311.02892.31993.348890.6813776.9183867.5990.286910.958611.2455377.061.192870.181790
水在飽和狀態之熱力性質
表3 展示水的飽和熱力學性質為溫度以從 -60 到200℃，由 Hyland 和 Wexler ( 1983b ) 描述的計算。表中的符號是依照標準蒸汽表名詞彙編的。 這些性質基於熱力學溫度尺標。 飽和液體水的焓和熵二者都是在三相點，0.01℃指定為0的。在水的三相點和臨界點溫度之間， 二種狀態—液態和汽態—可以在平衡中共存。這些狀態叫作飽和液態及飽和汽態。
在決定一些溼空氣性質項目時，主要地需求是飽和溼度比，水蒸汽飽和壓力。可以由表3得到或是由下面公式 (Hyland and Wexler 1983b)計算出來。
溫度範圍由-100到0℃冰的飽和壓力:
ln(pws)= C1/T+C2+C3T+C4 T2+C5T3 +C6T4+C7ln(T) (5)
其中
C1= -5.674 535 9 E+03
C2= 6.392 524 7 E+00
C3= -9.677 843 0 E-03
C4= 6.221 570 1 E-07
C5= 2.074 782 5 E-09
C6= -9.484 024 0 E-13
C7= 4.163 501 9 E+00
溫度範圍由0到200℃液態水的飽和壓力:
ln (pws) = C8/T+C9+C10T+C11T2+C12T3 +C13ln(T )(6)
其中
C8 = -5.800 220 6 E+03
C9 = 1.391 499 3 E+00
C10= -4.864 023 9 E-02
C11= 4.176 476 8 E-05
C12= -1.445 209 3 E-08
C13= 6.545 967 3 E+00
在方程式(5)和 (6)中，
ln = 自然對數
pws =飽和壓力， Pa
T =絕對溫度， K = ℃ + 273.15
方程式 ( 5 ) 和 ( 6 ) 的係數已經從 Hyland - Wexler 方程式得到了。由於來源中和在一些電腦計算精度中的誤差， 從方程式 ( 5 )和 ( 6 )得到的結果也許不是十分精確地符合表3所列的數值。
表3 水在飽和狀態之熱力性質
p
,
t
s
W
W
=
m
ws
ws
s
p
p
p
62198
.
0
W
-
=
p
,
t
s
x
x
=
f
p
,
t
s
w
w
p
p
=
f
絕對 比容, m3 /kg 焓, kJ/kg 熵, kJ/(kg．K)
溫度 壓力,
t, kPa Sat. Liquid Evap. Sat. Vapor Sat. Liquid Evap.Sat. Vapor Sat. Liquid Evap. Sat. Vapor Temp.,
℃ p vf/vf vfg/vfg vghf /hf hfg /hfg hg sf /sf sfg/sfgsg℃
)
p
/
p
)(
1
(
1
ws
m
-
-
m
=
f
-600.001080.00108290942.0090942.00-446.402836.272389.87-1.685413.306511.6211-60
-590.001240.00108279858.6979858.69-444.742836.462391.72-1.766713.245211.5677-59
-580.001410.00108270212.3770212.37-443.062836.642393.57-1.669813.814511.5147-58
-570.001610.00108261805.3561805.35-441.382836.812395.43-1.662013.124311.4623-57
-560.001840.00108254469.3954469.39-439.692836.972397.28-1.654213.064611.4104-56
-550.002090.00108248061.0548061.05-438.002837.132399.12-1.646413.005411.3590-55
-540.002380.00108242455.5742455.57-436.292837.272400.98-1.638612.946811.3082-54
-530.002710.00108337546.0937546.09-434.592837.422402.83-1.630812.888611.2578-53
-520.003070.00108333242.1433242.14-432.872837.552404.68-1.623012.830911.2079-52
-510.003480.00108329464.6729464.67-431.142837.682406.53-1.615312.773811.1585-51
-500.003940.00108326145.0126145.01-429.412837.802408.39-1.607512.717011.1096-50
-490.004450.00108323223.6923223.70-427.672837.912410.24-1.599712.660811.0611-49
-480.005030.00108320651.6820651.69-425.932838.022412.09-1.591912.605111.0131-48
-470.005680.00108318383.5018383.51-424.272838.122413.94-1.584212.549810.9656-47
-460.006400.00108316381.3516381.36-422.412838.212415.79-1.576412.494910.9185-46
-450.007210.00198414612.3514512.36-420.652838.292417.65-1.568612.440510.8719-45
-440.008110.00108413047.6513047.66-418.872838.372419.50-1.560912.386610.8257-44
-430.009110.00108411661.8511661.85-417.092838.442421.35-1.553112.333010.7799-43
-420.010220.00108410433.8510433.85-415.302838.502423.20-1.545312.279910.7346-42
-410.011470.0010849344.259344.25-413.502838.552425.05-1.537612.227310.6897-41
-400.012850.0010848376.338376.33-411.702838.602426.90-1.529812.175010.6452-40
-390.014380.0010857515.867515.87-409.882838.642428.76-1.522112.123210.6011-39
-380.016080.0010856750.366750.36-508.072838.671430.61-1.514312.071810.5575-38
-370.017960.0010856068.166068.17-406.242838.702432.46-1.506612.020810.5142-37
-360.020040.0010855459.825459.82-404.402838.712434.31-1.498811.970210.4713-36
-350.022350.0010854917.094917.10-402.562838.732436.16-1.491111.919910.4289-35
-340.024900.0010854432.364432.37-400.722838.732438.01-1.483311.870110.3868-34
-330.027710.0010853998.713998.71-398.862838.722439.86-1.475611.820710.3451-33
-320.030820.0010863610.713610.71-397.002838.712441.72-1.467811.771610.3037-32
-310.034240.0010863263.203263.20-395.122838.692443.57-1.460111.722910.2628-31
-300.038020.0010862951.642951.64-393.252838.662445.42-1.452411.674610.2222-30
-290.042170.0010862672.032672.03-391.362838.632447.27-1.444611.626610.1820-29
-280.046730.0010862420.892420.89-389.472838.592449.12-1.436911.479010.1421-28
-270.051740.0010862195.232195.23-387.572838.532450.97-1.429111.531810.1026-27
-260.057250.0010871992.151992.15-385.662838.482452.82-1.421411.484910.0634-26
-250.063290.0010871809.351809.35-383.742838.412454.67-1.413711.438310.0246-25
-240.069910.0010871644.591644.59-381.342838.342456.52-1.405911.39219.9862-24
-230.077160.0010871495.981495.98-379.892838.262458.37-1.398211.34629.9480-23
-220.085100.0010871361.941361.94-377.952838.172460.22-1.390511.30079.9102-22
-210.093780.0010871240.771240.77-376.012838.072462.06-1.382811.25559.8728-21
-200.103260.0010871131.271131.27-374.062837.972463.91-1.375011.21069.8356-20
-190.113620.0010881032.181032.18-372.102837.862465.76-1.367311.16619.7988-19
-180.124920.001088942.46942.47-370.132837.742467.61-1.359611.12189.7623-18
-170.137250.001088861.17861.18-368.152837.612469.46-1.351811.07799.7261-17
-160.150680.001088787.48787.49-366.172837.472471.30-1.344111.03439.6902-16
-150.165300.001088720.59720.59-364.182837.332473.15-1.336410.99109.6546-15
-140.181220.001088659.86659.86-362.182837.182474.99-1.328710.94809.6193-14
-130.198520.001089604.65604.65-360.182837.022476.84-1.321010.90539.5844-13
-120.217320.001089554.45554.45-358.172836.852478.68-1.323210.86299.5497-12
-110.237740.001089508.75508.75-356.152836.682480.53-1.305510.82089.5153-11
-100.259900.001089467.14467.14-354.122836.492482.37-1.297810.77909.4812-10
-90.283930.001089429.21429.21-352.082836.302484.22-1.290110.73759.4474-9
-80.309980.001090394.64394.64-350.042836.102486.06-1.282410.69629.4139-8
-70.338190.001090363.07363.07-347.992835.892487.90-1.274610.65529.3806-7
-60.368740.001090334.25334.25-345.932835.682489.74-1.266910.61459.3476-6
-50.401760.001090307.91307.91-343.872835.452491.58-2.259210.47419.3149-5
-40.437470.001090283.83283.83-341.802835.222493.42-1.251510.53409.2825-4
-30.476060.001090261.79261.79-339.722834.982495.26-1.243810.49419.2503-3
-20.517720.001091241.60241.60-337.632834.722497.10-1.236110.45449.2184-2
-10.562670.001091223.11223.11-335.532834.472498.93-1.228410.41519.1867-1
表3 水在飽和狀態之熱力性質
w
a
w
p
p
T
R
)
p
p
(
9645
.
28
RT
v
-
=
-
=
p
)
W
6078
.
1
1
(
T
R
p
964
.
28
)
W
6078
.
1
1
(
RT
v
a
+
=
+
=
*
t
186
.
4
t
805
.
1
2501
*)
t
t
(
*
W
*)
t
381
.
2
2501
(
W
s
-
+
-
-
-
=
w
1
2
1
2
h
W
W
h
h
=
-
-
絕對 比容, m3 /kg 焓, kJ/kg 熵, kJ/(kg．K)
溫度 壓力,
t, kPa Sat. Liquid Evap. Sat. Vapor Sat. Liquid Evap.Sat. Vapor Sat. Liquid Evap. Sat. Vapor Temp.,
℃ p vf/vf vfg/vfg vghf /hf hfg /hfg hg sf /sf sfg/sfgsg℃
)
p
/
p
f
)(
1
(
1
ws
s
m
-
-
m
=
f
00.611150.001091206.16206.16-333.432834.202500.77-1.220610.37609.15530
00.61120.001000206.141206.143-0.042500.812500.77-0.00029.15559.15530
10.65710.001000192.455192.4564.182498.432502.610.01539.11349.12861
20.70600.001000179.769179.7708.392496.052504.450.03069.07169.10222
30.75800.001000168.026168.02712.602493.682506.280.04599.03029.07613
40.81350.001000157.137157.13816.812491.312508.120.06118.98909.05014
50.87250.001000147.032147.03321.022488.942509.960.07638.94829.02445
60.93530.001000137.653137.65425.222486.572511.790.09138.90778.99906
71.00200.001000128.947128.94829.422484.202513.620.10648.86748.97387
81.07280.001000120.850120.85133.622481.842515.460.12138.82738.94888
91.14810.001000113.326113.32737.822479.472517.290.13628.78788.92459
101.22800.001000106.328106.32942.012477.112519.120.15118.74848.899510
111.31270.00100099.81299.81346.212474.742520.950.16598.70938.875211
121.40260.00100193.74393.74450.402472.382522.780.18068.67058.851112
131.49780.00100188.08888.08954.592470.022524.610.19538.63198.827213
141.59870.00100182.81582.81658.782467.662526.440.20998.59363.803514
151.70550.00100177.89777.89862.972465.302528.260.22448.55568.780115
161.81840.00100173.30773.30867.162462.932530.090.23898.51788.756816
171.93800.00100169.02169.02271.342460.572531.920.25348.48048.733817
182.06430.00100265.01765.01875.532458.212533.740.26788.44318.710918
192.19780.00100265.27461.27379.722455.852535.560.28218.40618.688319
202.33880.00100257.77457.77383.902453.482537.380.29648.36948.665820
212.48770.00100254.45054.50088.082451.122539.200.31078.33298.643621
222.64480.00100251.43351.43492.272448.752541.020.32498.29678.621522
232.81040.00100348.56248.56396.452446.392542.840.33908.26078.599623
242.98510.00100345.87245.873100.632444.022544.650.35318.22498.578024
253.16920.00100343.35043.351104.812441.662546.470.36728.18948.556525
263.36310.00100340.98540.986108.992439.292548.280.38128.15418.535226
273.56730.00100438.76638.767113.182436.922550.090.39518.11908.514127
283.78220.00100436.68236.683117.362434.552551.900.40908.08428.493228
294.00830.00100434.72634.727121.542432.172553.710.42298.04968.472429
304.24600.00100432.88932.889125.722429.802555.520.43678.01528.451930
314.49590.00100531.16031.161129.902427.432557.320.45057.98108.431531
324.75850.00100529.53529.536134.082425.052559.130.46427.94718.411232
335.03430.00100528.00628.007138.262422.672560.930.47797.91338.391233
345.32390.00100626.56726.568142.442410.292562.730.49157.87908.371334
355.62780.00100625.21225.213146.622417.912564.530.50517.84658.351635
365.94660.00100623.93523.936150.802415.532566.330.51867.81348.332036
376.28100.00100722.73322.734154.982413.142568.120.53217.78058.312737
386.63150.00100721.59921.600159.162410.762569.910.54567.74798.293438
396.99870.00100820.52920.530163.342408.372571.710.55907.71548.274439
407.38350.00100819.52019.521167.522405.982573.500.57247.68318.255540
417.78630.00100818.56718.568171.702403.582575.280.58577.65108.236741
428.20800.00100917.66717.668175.882401.192577.070.59907.61918.218142
438.64920.00100916.81816.819180.062398.792578.850.61227.58758.199743
449.11070.00101016.01416.015184.242396.392580.630.62547.35608.181444
459.59320.00101015.25515.256188.422393.992582.410.63867.52478.163245
4610.09760.00101014.53714.538192.602391.592584.190.65177.49368.145246
4710.62460.00101113.85813.859196.782389.182585.960.66487.46268.127447
4811.17510.00101113.21413.215200.972386.772587.740.67787.43198.109748
4911.75000.00101212.60612.607205.152384.362589.510.69087.40138.092149
5012.34990.00101212.02912.029209.332381.942591.270.70387.37098.074750
5112.97590.00101311.48211.483213.512379.532593.040.71677.34078.057451
5213.62900.00101310.96410.965217.702377.102594.800.72967.31078.040352
5314.31000.00101410.47310.474221.882374.682596.560.74247.28098.023353
5415.02000.00101410.00110.008226.062372.262598.320.75527.25128.006454
5515.75970.0010159.5639.5663230.252369.832600.070.76807.22177.989755
5616.53040.0010159.1479.1468234.432367.392601.820.78077.19247.973156
5717.33310.0010168.7448.7489238.612364.962603.570.79347.16327.956657
5818.16900.0010168.36908.3700242.802362.522605.320.80617.13427.940358
表3 水在飽和狀態之熱力性質
742
.
0
819
.
9
284
.
7
m
m
2
1
3
1
m
m
3
1
2
3
3
a
2
a
2
a
1
a
=
=
=
-
-
=
-
-
線
線
或
線
線
ws
s
ws
s
s
p
f
p
p
f
62198
.
0
W
-
=
w
w
w
s
1
2
1
2
m
)
h
m
(
q
W
W
h
h
å
å
+
=
-
-
)
water
(
kg
/
kJ
8555
0015
.
0
52
.
2555
0015
.
0
9
W
h
=
´
+
=
D
D
絕對 比容, m3 /kg 焓, kJ/kg 熵, kJ/(kg．K)
溫度 壓力,
t, kPa Sat. Liquid Evap. Sat. Vapor Sat. Liquid Evap.Sat. Vapor Sat. Liquid Evap. Sat. Vapor Temp.,
℃ p vf/vf vfg/vfg vghf /hf hfg /hfg hg sf /sf sfg/sfgsg℃
)
air
dry
(
s
/
kg
856
.
0
0
.
39
0
.
54
)
52
.
2555
0015
.
0
(
9
h
h
)
h
m
(
q
m
2
1
w
w
s
a
=
-
´
+
=
-
å
+
=
5919.03870.0010178.00948.0114246.992360.082607.060.81877.10547.924059
6019.9440.0010177.66777.6697251.172357.632608.800.83137.07677.907960
6120.8850.0010187.34287.3438255.362355.192610.540.84387.04827.892061
6221.8640.0010187.03377.0347259.542352.732612.280.85637.01987.876162
6322.8820.0010196.73976.7407263.732350.282614.010.86886.99167.860463
6423.9400.0010196.45996.4609267.922347.822615.740.88126.96367.844864
6525.0400.0010206.19356.1946272.112345.362617.460.89366.93577.829365
6626.1800.0010205.93975.9409276.302342.892619.190.90606.90807.814066
6727.3660.0010215.69825.6992280.492340.422620.900.91836.88047.798767
6828.5960.0010225.46805.4690284.682337.952622.620.93062.85307.783668
6929.8730.0010225.24855.2495288.872335.472624.330.94296.82577.768669
7031.1980.0010235.03925.0402293.062332.992626.040.95516.79867.753770
7132.5720.0010234.83964.8407297.252330.502627.750.96736.77167.738971
7233.9970.0010244.64924.6502301.442328.012629.450.97956.74487.724272
7335.4750.0010254.46754.4685305.632325.512631.150.99166.71817.709773
7437.0060.0010254.29404.2951309.832323.022632.841.00376.69157.695274
7538.5920.0010264.12844.1294314.022320.512634.531.01576.66517.680975
7640.2360.0010263.97023.9712318.222318.012636.221.02786.63897.666676
7741.9380.0010273.81903.8201322.412315.492637.901.03986.61277.652577
7843.7000.0010283.67463.6756326.612312.982639.581.05176.58677.638478
7945.5240.0010283.53653.5375330.812310.462641.261.06366.56097.624579
8047.4120.0010293.40443.4055335.002307.932642.931.07556.53517.610780
8149.3640.0010303.27813.2792339.202305.402644.601.08746.50957.596981
8251.3840.0010303.15733.1583343.402902.862646.261.09936.48417.583382
8353.4730.0010313.04173.0427347.602300.322647.921.11116.45877.569883
8455.6330.0010322.93102.9320351.802297.782649.581.12286.43357.556384
8557.8650.0010322.82502.8260356.012295.222651.231.13466.40847.543085
8660.1710.0010332.72352.7245350.212292.672652.881.14636.38347.529786
8762.5540.0010342.62632.6273364.412290.112654.521.15806.35867.516687
8865.0150.0010352.53312.5341368.622287.542656.161.16966.33397.503588
8967.5560.0010352.44382.4448372.822284.972657.791.18126.30937.490589
9070.1800.0010362.35822.3592377.032282.392659.421.19286.28487.477690
9172.8880.0010372.27602.2771381.242279.812661.041.20446.26057.464891
9275.6830.0010372.19732.1983385.452277.222662.661.21596.23627.452192
9378.5660.0010382.12172.1228389.662274.622664.281.22746.21217.439593
9481.5410.0010392.04922.0502393.872272.022665.891.23896.18817.427094
9584.6080.0010401.97961.9806398.082269.412667.491.25046.16427.414695
9687.7700.0010401.91281.9138402.292266.802669.091.26186.14047.402296
9791.0300.0010411.84861.8496406.512264.182670.691.27326.11687.389997
9894.3900.0010421.78691.7880410.722261.552672.281.28456.09327.377798
9997.8520.0010441.72771.7287414.942258.922673.861.29596.06977.365699
100101.4190.0010441.67081.6718419.162256.282675.441.30726.04647.3536100
101105.0920.0010441.61611.6171423.382253.642677.021.31856.02327.3416101
102108.8750.0010451.56351.5645427.602250.992678.581.32976.00007.3298102
103112.7700.0010461.51291.5139431.822248.332680.151.34105.97707.3180103
104116.7790.0010471.46421.4652436.042245.662681.711.35225.95417.3062104
105120.9060.0010471.41741.4184440.272242.992683.261.36345.93137.2946105
106125.1520.0010481.37231.3734444.492240.312684.801.37455.90867.2830106
107129.5200.0010491.32901.3300448.722237.632686.351.38565.88607.2716107
108134.0120.0010501.28721.2883452.952234.932687.881.39675.86357.2601108
109138.6330.0010511.24701.2481457.182232.232689.411.40785.84107.2488109
110143.3840.0010521.20831.2093461.412229.522690.931.41885.81877.2375110
111148.2670.0010521.17101.1720465.642226.812692.451.42985.79657.2263111
112153.2870.0010531.13501.1361469.882224.092693.961.44085.77447.2152112
113158.4450.0010541.10041.1015474.112221.352695.471.45185.75247.2402113
114163.7450.0010551.06701.0681478.352218.622696.971.46275.73047.1931114
115169.1900.0010561.03481.0359482.592215.872698.461.47375.70867.1822115
116174.7820.0010571.00381.0048486.832213.122699.951.48465.68687.1714116
117180.5250.0010580.97390.9749491.072210.352701.431.49545.66527.1606117
118186.4200.0010590.94500.9460495.322207.582702.901.50635.64367.1499118
表3 水在飽和狀態之熱力性質
701
.
0
)
52
.
2555
0015
.
0
(
9
9
)
h
m
(
q
q
H
H
w
w
s
s
t
s
=
´
+
=
å
+
D
D
2
a
1
a
1
3
3
2
1
3
3
2
m
m
W
W
W
W
h
h
h
h
=
-
-
=
-
-
p
,
t
s
W
W
=
m
w
a
w
p
p
T
R
)
p
p
(
9645
.
28
RT
v
-
=
-
=
絕對 比容, m3 /kg 焓, kJ/kg 熵, kJ/(kg．K)
溫度 壓力,
t, kPa Sat. Liquid Evap. Sat. Vapor Sat. Liquid Evap.Sat. Vapor Sat. Liquid Evap. Sat. Vapor Temp.,
℃ p vf/vf vfg/vfg vghf /hf hfg /hfg hg sf /sf sfg/sfgsg℃
p
,
t
s
x
x
=
f
119192.4730.0010590.91710.9182499.562204.802704.371.51715.62217.1392119
120198.6850.0010600.89020.8913503.812202.022705.831.52795.60077.1286120
122211.6010.0010620.83910.8402512.312196.422706.731.54945.55827.1076122
124225.1940.0010640.79160.7927520.822190.782711.601.57095.51607.0869124
126239.4900.0010660.74720.7483529.332185.112714.441.59225.47427.0664126
128254.5150.0010680.70570.7068537.862179.402717.261.61355.43267.0461128
130270.2980.0010700.66700.6681546.392173.662720.051.63475.39147.0261130
132286.8660.0010720.63080.6318554.932167.872722.801.65575.35057.0063132
134304.2470.0010740.59690.5979563.482162.052725.531.67675.30996.9867134
136322.4700.0010760.56510.5662572.042156.182728.221.69775.26976.9673136
138341.5660.0010780.53540.5364580.602150.282730.881.71855.22966.9481138
140361.5650.0010800.50750.5085589.182144.332733.511.73935.18996.9292140
142382.4970.0010820.48130.4824597.762138.342736.111.75995.15056.9104142
144404.3940.0010840.45670.4578606.362132.312738.671.78055.11136.8918144
146427.2880.0010860.43360.4347614.972126.232741.191.80115.07246.8735146
148451.2110.0010880.41190.4130623.582120.102743.681.82155.03386.8553148
150476.1980.0010910.39140.3925632.212113.922746.131.84194.99546.8373150
152502.2810.0010930.37220.3733640.852107.702748.551.86224.95736.8194152
154529.4950.0010950.35410.3552649.502101.432750.931.88244.91946.8017154
156557.8750.0010970.33700.3381658.162095.112753.271.90264.88176.7842156
158587.4560.0011000.32090.3220666.832088.732755.571.92264.84436.7669158
160618.2750.0011020.30580.3069675.522082.312757.821.94274.80706.7497160
162650.3680.0011040.29140.2925684.222075.822760.041.96264.77016.7327162
164683.7720.0011070.27790.2790692.932069.292762.221.98254.73336.7158164
166718.5260.0011090.26510.2662701.652062.702764.352.00234.69676.6990166
168754.6670.0011120.25300.2541710.392056.052766.442.02214.66036.6824168
170792.2350.0011140.24150.2427719.142049.342768.482.04184.62426.6659170
172831.2680.0011170.23070.2318727.912042.572770.482.06144.58826.6496172
174871.8080.0011190.22050.2216736.692035.742772.432.08104.55246.6334174
176913.8940.0011220.21070.2119745.482028.852774.332.10054.51686.6173176
178947.5680.0011250.20150.2026754.292021.892776.192.12004.48136.6013178
1801002.8710.0011270.19280.1939763.122014.872777.992.13944.44606.5854180
1821049.8460.0011300.18450.1856771.962007.782779.742.15874.41096.5691182
1841098.5350.0011330.17660.1777780.822000.632781.452.17804.37606.5540184
1861148.9820.0011360.16910.1703789.691993.402783.102.19734.34126.5385186
1881201.2300.0011390.16200.1632798.591986.112784.702.21654.30656.5230188
1901255.3240.0011410.15530.1564807.501978.742786.242.23564.27206.5076190
1921311.3090.0011440.14880.1500816.431971.302787.722.25474.23766.4924192
1941369.2300.0011470.14270.1439825.371963.782789.152.27384.20346.4772194
1961429.1330.0011500.13690.1380834.341956.192790.522.29284.16936.4621196
1981491.0660.0011530.13140.1325843.321948.522791.832.31184.13536.4471198
w
w
p
p
p
62198
.
0
W
-
=
2001555.0740.0011570.12610.1272852.331940.762793.092.33074.10146.4321200
濕度的參數
既定溼空氣樣品的溼度比（亦可稱為水分含量或混合比）W被定義為樣品中水蒸汽的質量對乾空氣質量的比值。
W = mw / m a(7)
溼度比（humidity ratio）W 等於摩爾分數比 x w/x a 乘上分子量的比值；即是： 18.01528/28.9645 = 0.62198,換言之:
W = 0.62198 x w/x a (8)
比濕度（specific humidity）q是樣品的水蒸汽質量對濕空氣總質量的比值：
q = mw/(mw + ma) (9a)
轉換成溼度比項:
q = W/(1 + W)(9b)
絕對濕度（absolute humidity）(亦可稱為水蒸汽密度) dw 是樣品的水蒸汽質量對濕空氣總體積的比值：
dw = mw/V(10)
濕空氣混合物的密度（density）ρ總質量對總體積的比值：
ρ=(m a+ mw)/V=(1+v)/ W(11)
其中
v 是濕空氣的比容（specific volume）， m3/kg (dry air)， 像(27)式一樣的定義。
涉及飽和的濕度參數
以下濕度參數的定義涉及了濕空氣的概念：
飽和溼度比（saturation humidity ratio）Ws (t， p)是在相同溫度t及壓力p下關於水（或冰）的濕空氣飽和狀態溼度比。
飽和度（Degree of saturation） μ是在相同溫度t及壓力p空氣溼度比W 與飽和溼度比Ws 的比值：
62198
.
0
/
W
)
1
(
1
s
f
-
+
f
=
m
ws
ws
s
p
p
p
62198
.
0
W
-
=
(12)
相對濕度（Relative humidity）ψ是在既定的空氣樣品下水蒸汽的摩爾分數x w 與相同溫度及壓力的飽和水蒸汽摩爾分數x ws的比值
(13)
結合方程式 (8)、(12)、及 (13)：
p
,
t
s
w
w
p
p
=
f
(14)
露點溫度（Dew-point temperature）td是溼空氣在相同的壓力p 飽合，且與溼空氣既定樣品有相同的溼度比W時的溫度。 解td(p，W)的方程式定義為：
Ws (p ，td) = W (15)
熱力溼球溫度（Thermodynamic wet-bulb temperature）t*，水（液態或是固態）蒸發進入既定的乾球溫度t及濕度比W之濕空氣中，當壓力p維持定值，在相同的溫度t*下，能將空氣絕熱地帶入飽和狀態。這項參數將在後面章節個別的考慮。
乾空氣及濕空氣的理想氣體關係式
當將濕空氣看成各別的理想氣體、乾空氣及水蒸汽，每一成份假設均使可用理想氣體狀態方程式如下：
乾空氣 paV = naRT(16)
水蒸汽 pwV = nwRT(17)
其中
pa = 乾空氣分壓
pw =水蒸汽分壓
V =總混合體積
na =乾空氣之摩爾數
n w =水蒸汽之摩爾數
R = 通用氣體常數 8314.41 J/(kg mol．K)
T = 絕對溫度， K
混合氣體也可使用理想氣體：
pV = nRT(18)
或是
(pa + pw) V = (na+ n w) RT(19)
其中 p = pa + pw是混合氣體總壓力，n = na+ n w 是混合氣體總摩爾數。
從方程式(16)到(19)， 乾空氣及水蒸汽的摩爾分數分別為：
xa = pa/(pa + pw)= pa/p(20)
和
xw = pw/(pa + pw)= pw/p(21)
從方程式(8)、 (20)、及(21)， the 濕度比 W 可寫成：:
)
p
/
p
)(
1
(
1
ws
m
-
-
m
=
f
(22)
飽和度μ被方程式(12)定義成：
*
t
186
.
4
t
805
.
1
2501
*)
t
t
(
*
W
*)
t
381
.
2
2501
(
W
s
-
+
-
-
-
=
其中
p
)
W
6078
.
1
1
(
T
R
p
964
.
28
)
W
6078
.
1
1
(
RT
v
a
+
=
+
=
(23)
pws項代表在空氣不存在的既定溫度t下水蒸汽飽和壓力，這壓力p只是溫度的函數，與在飽和濕空氣下之水蒸汽壓力略有不同。
相對濕度ψ被方程式(13)定義成：
ws
s
ws
s
s
p
f
p
p
f
62198
.
0
W
-
=
)
p
/
p
f
)(
1
(
1
ws
s
m
-
-
m
=
f
以方程式(21)代替xw及 x ws：
(24)
以方程式(21) 代替方程式(14)中x ws：
(25)
φ及μ在乾空氣時是均為零，在飽和濕度時均是1。在中間狀態且較高溫度時，他們的值大不相同。
濕空氣混合物之比容v 被表示成乾空氣單位質量術語，即：
v=V/ma=V/(28.9645na) (26)
其中 V 是混合空氣的總容積， ma是乾空氣的總質，及na是乾空氣的摩爾數。由方程式(16)和 (26)及p = pa + pw之關係可得：
(27)
利用方程式(22):
(28)
在方程式(27)及(28)中， v是比容， T 是絕對溫度， p 是總壓力， pw是水蒸汽分壓，和W是濕度比。
在比單位方程式(28)可被表示成：
v = 0.2871 (t + 273.15 ) (1+ 1.6078W )/p
其中
v = 比容， m3 /kg
t = 乾球溫度，℃
W = 濕度比， kg (水)/kg (乾空氣)
p = 總壓力， kPa
混合之理想氣體焓值（enthalpy）等於各個成份焓值的總和。因此濕空氣的焓值可以寫成：
h =ha+ Whg(29)
其中 ha 是乾空氣的比焓；hg 是在混合氣體溫度下飽和水蒸汽之比焓。近似是：
ha = 1.006t (kJ/kg)(30)
hg = 2501+1.805t (kJ/kg ) (31)
其中 t 乾球溫度，℃。則濕空氣的比焓變成：
h = 1.006t +W(2501 + 1.805t) (kJ/kg) (32)
熱力溼球溫度和露點溫度
對於溼空氣的任何狀態，存在一溫度點t*，處於該狀態點之液態(或者固態)水在完全相同的溫度和壓力下蒸發到空氣中，把它帶到飽和狀態( Harrison 1965 )。在絕熱飽和過程期間，飽和空氣以等於注射水的溫度被排出(圖 8和 9 )。在定壓過程中，在相對應於飽和狀態溫度t*，溼度比從一個既定的初始值W增加到Ws*；在相對應於飽和狀態溫度t*，從一個既定的初始比焓h 增加到hs* ；每單位質量乾空氣所增加水的質量是( Ws* -W )，它增加到溼空氣中的能量是( WS * -W)hw*，hw* 代表在t*時因水所增加的比焓。因此，若過程是完全地絕熱，則在定壓下焓的守恆式是：
h+(Ws* -W)hw* =hs*(33)
當壓力固定時，性質Ws*， hw*， and hs* 只是溫度t*的函數。在既定的h、W、和 p時， t*能滿足方程式(33)是為熱力濕球溫度。.
乾濕球溫度計(psychrometer)是由兩支溫度計所組合成的，由已經用水弄得溼透的芯心覆蓋在其中一個溫度計上。當把這個溼球泡放在氣流裡時，水從蕊心蒸發，最後會達到一個平衡的溫度稱為濕球溫度。
這個過程不是在定義熱力溼球溫度時所稱絕熱飽和過程中的一個， 它， 但是同時由濕球泡傳遞熱量及質量。 由Lewis關係描述了這個過程的基本機制 ( 第5章 ) 。幸好，在應用濕球溫度計讀值到熱力濕球溫度只有很小的修正量。
如同定義那樣，熱力溼球溫度是既定溼空氣樣品的獨特性質，與測量技術無關。
方程式 (33) t*是精確的，因為它定義熱力溼球溫度。將近似理想氣體關係式[方程式(32)]中h代入，同樣的表示hs*， 及相似的關係式：
h w*= 4.186t* (kJ/kg )(34)
代入方程式 (33)， 及解出濕度比：
(35)
其中t與t*是以℃表示。
在濕度比W及壓力p濕空氣的露點溫度（dew-point temperature）td在前面被定義為Ws(p，td) 的解td(p，W)。若是理想氣體，簡化為：
pws(td)=pw=(pW)/(0.62198+W)
(36)
其中pw是濕空氣樣品中水蒸汽分壓，pws(td)是在溫度td時飽和蒸汽壓力。飽和蒸汽壓力可以從表3或是方程式(5)或(6)得到。露點溫度能被下列兩個方程式之一直接計算(Peppers 1988)：
當露點溫度範圍在0到93℃時：
td=C14+C15α+C16α2+C17α3+C18(Pw)0.1984 (37)
和露點溫度低於0℃時：
td=6.09+12.608α+0.4959α2
(38)
其中
td=露點溫度，℃
α=ln(Pw)
Pw=水蒸汽分壓，kPa
C14=6.54
C15=14.526
C16=0.7389
C17=0.09486
C18=0.4569
溼空氣性質的數值計算
下面是引用已經提過的方程式及表，並利用理想氣體關係式計算濕空氣性質的概要。對大部分空調工程實務計算而言，這些關係式是足夠精確的，且手算或是電腦計算均適合。更詳細可參考第一章的表15到18 Olivieri (1996) 。圖解的步驟在濕空氣圖的章節內將被討論。
狀況1.
已知: 乾球溫度t， 濕球溫度t*， 壓力 p
需得到 使用註解
pws (t*) Table 3 or Eq. (5) or (6) Sat. press. for temp. t*
Ws * Eq. (23) Using pws (t*)
WEq. (35)
p ws (t) Table 3 or Eq. (5) or (6) Sat. press. for temp. t
Ws Eq. (23) Using pws (t)
μ Eq. (12) Using Ws
ψEq. (25) Using pws (t)
v Eq. (28)
h Eq. (32)
pwEq. (36)
tdTable 3 with Eq. (36)， (37)， or (38)
狀況2.
已知: 乾球溫度t， 露點溫度td， 壓力 p
需得到 使用註解
pw=pws (td) Table 3 or Eq. (5) or (6)Sat. press. for temp. td
W Eq. (22)
pws (t) Table 3 or Eq. (5) or (6) Sat. press. for temp. td
Ws Eq. (23) Using pws (t)
μ Eq. (12) Using Ws
ψ Eq. (25) Using pws (t)
v Eq. (28)
h Eq. (32)
t* Eq. (23) and (35) with Table 3 or Requires trial-and-error or numerical
with Eq. (5) or (6) solution method
狀況3.
已知: 乾球溫度t， 相對濕度ψ，壓力 p
需得到 使用註解
pw=pws (td) Table 3 or Eq. (5) or (6) Sat. press. for temp. t
pwEq. (24)
W Eq. (22)
Ws Eq. (23) Using pws (t)
μ Eq. (12) Using Ws
v Eq. (28)
h Eq. (32)
tdTable 3 with Eq. (36)， (37)， or (38)
t* Eq. (23) and (35) with Table 3 or Requires trial-and-error or numerical
with Eq. (5) or (6) solution method
WS及ψ精確關係之計算
修正說明(1)液化的氣體對凝結相性質的影響；(2) 壓力對凝結相性質的影響； 和(3)分子之間力量對濕氣本身的性質的影附，應用於方程式 (23) 或者 (25) :
(23a)
(23b)
表4 列出在壓力及溫度組合下fs值。Hyland and Wexler (1983a) 給予增加值。
表4 fs 值及估計最大不可靠性 (EMU)
0.1 MPa 0.5 MPa 1 MPa
EMU
EMU EMU
T， K f E+04 f E+04 f E+04
173.15 1.0105 134 1.0540 66 1.1130 136
273.15 1.0039 2 1.0177 10 1.0353 19
373.15 1.0039 0.1 1.0180 4 1.0284 11
用於標準壓力之濕空氣性質表
表 2 為在-60 to 90℃之標準大氣壓熱力性質表。中間的濕空氣狀態性質可以用飽和度計算：:
比容 v= va+μvas (39)
焓 h =ha +μhas(40)
熵 s =sa +μsas (41)
這些方程式可精確到 70℃. 在更高的溫度， 誤差就需注意。Hyland and Wexler (1983a) 可以估算在標準大氣壓下v， h， and s 的誤差。
濕空氣線圖
一個濕空氣線用圖表表示溼空氣的熱力性質。
空氣線圖座標的選擇是隨心所欲的。一個以比焓及濕度比為座標的圖以最小的熱力接近值提供許多濕空氣問題上便利的圖解。ASHRAE發展了七個這樣的空氣線圖。
線圖1到4是用於海平面壓力（101.325kPa）。線圖5是用於海拔750m高度（92.66kPa）。線圖6是用於海拔1500m高度（84.54kPa）。線圖7是用於海拔2250m高度（77.04kPa）。所有線圖都是使用比焓及濕度比的斜角座標，而且都與表2及Goff 和 Gratch (1945， 1949)計算性質方法所得的一致，並Hyland and Wexler (1983a)也致。Palmatier (1963)描繪線圖的幾何架構特別應用於線圖一和四。
這些線圖之乾球溫度範圍是：
線圖1、5、6、7一般溫度 0 to 50℃
線圖 2低溫 -40 to 10℃
線圖 3高溫 100 to 120℃
線圖 4 非常高溫 100 to 200℃
其他大氣壓力之濕空氣性質或是線圖可以用內插法求得。就大部份的目的，足夠的精確值可以由本節之理想氣體關係得到。線圖上海拔高度的架構已經由Haines (1961)、Rohsenow (1946)、及 Karig (1946)處理過。
覆蓋表框(overlay reveals)下線圖1及6的比較：
1. 乾球溫度是一致的。
2. 既定的濕球溫度來自同樣的乾球溫度線及兩個飽和曲線的交點，它們有相同的斜率。
3. 因海拔高度，在既定的乾球溫度及濕球溫度下，濕度比及比焓均增加，但是相對濕度有些微的變化。
4. 在既定的乾球溫度及濕度比下，體積改變快速，幾乎反比於大氣壓力。
下表比較在海平面（線圖1）及1500m（線圖6）之性質
線圖
db
wb
h
W
rh
v
1
40
30
99.5
23.0
49
0.920
6
40
30
114.1
28.6
50
1.111
圖一是ASHRAE濕空氣線圖中的線圖1，它展示濕度比線（水平線）從0（乾空氣）到30g（moisture）/kg(dry air)。每條畫過線圖的焓線均是精確平行的斜線。
乾球溫度線是直線，並不精確平行於其他任一條乾球溫度線，且些微從垂直位置傾斜。熱力濕球溫度線是方向稍些與焓線不同的斜線。它們同樣是直線但並不精確平行於其他任一條線。
相對濕度（rh）線是以每間隔10％展示。飽和曲線是100％的曲線，當 W=0（乾空氣）的水平線即是0％的相對濕度曲線。
比容線是直線但並不精確平行於其他任一條線。
為溼空氣的霧氣條件已經發展出了在飽和曲線上方的狹窄地區。這個兩相區表示飽和溼空氣和液態水的物理性混合物，而兩成份處於熱平衡中。霧區的等溫線與熱力溼球溫度線的延伸相符合。如果需要，可以由溼度比、焓、和熱力溼球溫度線的延伸使霧區進一步擴展。
線圖左邊的半圓規展示了二個尺標—一個是顯熱–總熱比，另一個為焓差值與溼度比差值的比值。 用這個半圓規來制定濕空氣線圖上狀態線的方向。
例題1說明使用ASHRAE濕空氣線圖決定濕空氣的性質。
例題1 濕空氣在40℃乾球溫度，20℃熱力濕球溫度，及101.325kPa壓力。試決定濕度比、焓、露點溫度、相對濕度、及比容。
解：把狀態點置於線圖1(圖1 ) 之40℃乾球溫度和20℃熱力溼球溫度的相點上。讀取W = 6.5 g / kg(dry air) 。
由用兩個三角板來畫最靠近的焓線平行線[ 60 kJ/kg (dry air)] 找到焓透過對最靠近的邊尺的狀態點。 讀值h = 56.7 kJ/kg (dry air)。
露點溫度能夠在W = 6.5 g(moisture) / kg (dry air) 與 飽和曲線的交點被讀取。td=7℃。
相對濕度ψ可以直接得到。ψ=14％。
比容可以在比容線0.80及0.90m3/kg(dry air)之間以線性之內插法得到。v=0.896 m3/kg(dry air)。
典型空氣調節過程
ASHRAE濕空氣線可用於解決許多濕空氣過程的問題。透過例題說明的使用是最佳的解說。在下面例題，過程都發生在101.325kPa的定壓力上
濕空氣加熱
單獨的加熱濕空氣過程在ASHRAE濕空氣線圖被表示成水平線，因為濕度比保持不變。
圖2展示一個’加熱到濕空氣流的裝置。在穩流狀況下，所需增加的熱量是：
1q2=ma(h2-h1)(42)
例題2 濕空氣在2℃飽和，10m3/s的風量進入加熱盤管，空氣離開盤管的溫度為40℃。求所需加熱量。
解：圖3 顯示了解答。狀態1是位於2℃飽和曲線上。因此h1 =12.5 kJ/kg (dry air)，W1= 6.5 g(moisture) / kg (dry air)及v1=0.896 m3/kg(dry air)。狀態2是位於t=40℃及W2= W1= 6.5 g(moisture) / kg (dry air)的交點上。因此，h2 =51.4 kJ/kg (dry air)。乾空氣的質量流率為：
ma=10/0.785=12.74kg/s(dry air)
從方程式(42)：
742
.
0
819
.
9
284
.
7
m
m
2
1
3
1
m
m
3
1
2
3
3
a
2
a
2
a
1
a
=
=
=
-
-
=
-
-
線
線
或
線
線
1q2=12.74(51.4-12.5)=496 kW
濕空氣冷卻
w
1
2
1
2
h
W
W
h
h
=
-
-
當使溼空氣被冷卻到初始的露點溫度以下時，會發生水份的分離。圖4 顯示了若溼空氣被冷卻盤管均一地(uniformly)處理。雖然能夠使水從初始露點到最後飽和溫度不同的溫度範圍分離， 但是假設在它從系統排出前凝結水已冷卻到最後空氣溫度t2。
圖4系統的穩流能量及質量方程式是：
ma=mah2+1q2 +mwhw2
maW1=maW2+mw
因此：
mw= ma(W1-W2)(43)
1q2 =ma〔(h1 - h2)- (W1-W2) hw2) (44)
例題3 濕空氣在30℃乾球溫度及50％相對濕度狀態下，以5m3/s的風量進入冷卻盤管被冷凝到10℃的最後飽和狀態。求所需冷凍量 kW。
解：圖5 顯示了解答。狀態1是位於狀態點置於t=30℃和及ψ=50％的相點上。因此，h1 =64.3 kJ/kg (dry air)，W1= 13.3 g(moisture) / kg (dry air)及v1=0.877 m3/kg(dry air)。狀態2是位於10℃的飽和曲線上。因此，h2 =29.5 kJ/kg (dry air)及W2= 7.66 g(moisture)/kg (dry air)。從表2查出h2 =42.01 kJ/kg (water)。乾空氣的質量流率為：
ma=5/0.877=5.70kg/s(dry air)
從方程式(44)：
1q2 =5.70〔(64.3-29.5)-(0.0133-0.00766)42.01〕=197 kW
兩股濕空氣流的絕熱混合
在空調系統常見的過程是兩股濕空氣流的絕熱混合，圖6顯示了這個問題。絕熱混合被三個方程式管制：
ma1h1+ma2h2=ma3h3
ma1+ma2=ma3
ma1W1+ma2W2=ma3W3
消去ma3得到：
(45)
依照上式，在ASHRAE線圖上，混合後的空氣狀態點會位於兩股空氣流狀態點的連接線上，並以兩股氣流相同的乾空氣質量比將此連接線分割成兩部分。
)
water
(
kg
/
kJ
8555
0015
.
0
52
.
2555
0015
.
0
9
W
h
=
´
+
=
D
D
例題4 2m3/s的室外空氣在4℃乾球溫度及2℃熱力濕球溫度狀態下，與25℃乾球溫度及50％相對濕度、6.25m3/s的循環空氣絕熱混合。求混合後空氣的乾球溫度及熱力濕球溫度。
解：圖7 顯示了解答。狀態1及狀態2是位於ASHRAE線圖上，可知v1=0.789 m3/kg(dry air)及v2=0.858 m3/kg(dry air)。因此：
ma1=2/0.789=2.535kg/s(dry air)
ma2=6.25/0.858=7.284kg/s(dry air)
從方程式(45)：
w
w
w
s
1
2
1
2
m
)
h
m
(
q
W
W
h
h
å
å
+
=
-
-
701
.
0
)
52
.
2555
0015
.
0
(
9
9
)
h
m
(
q
q
H
H
w
w
s
s
t
s
=
´
+
=
å
+
D
D
結果，1—3部分線長是0.742乘以整條線長1—2。利用直尺，定位狀態3，並求出t3=19.5℃及t3*=14.6℃。
水噴灑到濕空氣之絕熱混合
蒸汽或水被噴灑到濕空氣流中以增加它的濕度。圖8表示一般空調過程的示意圖。如果這混合是絕熱的，可應用方程式：
ma1h1+mwhw=ma2h2
ma1W1+mw=ma2W2
因此，
)
air
dry
(
s
/
kg
856
.
0
0
.
39
0
.
54
)
52
.
2555
0015
.
0
(
9
h
h
)
h
m
(
q
m
2
1
w
w
s
a
=
-
´
+
=
-
å
+
=
(46)
依照上式，在ASHRAE線圖上，濕空氣最後狀態點會位直線上，此直線畫經始狀態點，方向則被噴灑水的比焓所固定。
例題5 20℃乾球溫度及8℃熱力濕球溫度的濕空氣，被絕熱噴灑的110℃飽和蒸汽處理到露點溫度為13℃。空氣的質量流率為2kg/s。求濕空氣最後的乾球溫度及蒸汽的質量流率。
解：圖9 顯示了解答。從表3可知濕飽和蒸汽之焓值hg=2691kJ/kg(water)。因此，依照方程式(46)，位於ASHRAE線圖上連接狀態1及狀態2之狀態線是必須有一個方向：
Δh/ΔW=2.691 kJ/g(water)
利用Δh/ΔW半圓規畫製狀態線。首先，在半圓規上連接原點及Δh/ΔW=2.691以建立參考線。經過濕空氣初始狀態點畫第二條平行於參考線之直線。這二條直線就是狀態線，狀態2被建立於狀態線及飽和曲線在13℃水平延長線的交點(td2=13℃)。因此，t2=20.2℃。
W2及W1的值可以由線圖讀取。則需要的蒸汽量：
Mw=ma(W2-W1)=2×1000(0.0094-0.0018)=15.2g/s(steam)
空間熱吸收及濕空氣之濕氣獲得
空氣調節一個空間的問題通常是取決於(1)需供應濕空氣的數量，(2)在特殊條件下空調所要從空間內移掉既有的能量及水份的總量。
圖10顯示一個能量及濕氣流率增加的空間。熱量qs代表空間內的淨總熱得量，是從空間邊界傳入及內部熱源產生而增加。熱得涉及能量的獨自增加且不包括由於水（或水蒸汽）所提供的能量。一般稱為顯熱得（sensible heat gain）。Σmw代表空間內的淨總濕氣獲得量，是從空間邊界傳入及內部產生而增加。每公斤的濕氣注入空間內所增加的能量等於它的比焓。
假設穩狀條件，決定的方程式是：
mah1+qs+Σmwhw=mah2
maW1+Σmw=maW2
或
qs+Σmwhw=ma(h2-h1)(47)
Σmw=ma(W2-W1)(48)
方程式(47)代表從所有來源加增加到空間的總能量，由方程式(47)及(48)：
2
a
1
a
1
3
3
2
1
3
3
2
m
m
W
W
W
W
h
h
h
h
=
-
-
=
-
-
(49)
依照上式，在ASHRAE線圖上及離開的空氣的既定狀況，所有可能的狀況（條件）供應空氣必須落在經過離開空氣的狀態點的直線上，此直線方向由〔qs+Σ(mwhw)/ Σmw〕的數值決定。這條線即為既定問題的狀態線。
例題6 25℃乾球溫度及19℃熱力濕球溫度的濕空氣從房間內被抽離，空間內的顯熱獲得量是 9 kW。濕氣獲得是由空間內的人所產生的，0.0015kg/s。假設濕氣為30℃的飽和水蒸汽。15℃的濕空氣被引入房間內。求所需熱力濕球溫度及供應空氣的體積流率。
解：圖11 顯示了解答。狀態2位於ASHRAE線圖上，從表3可知增加水蒸汽之比焓hg=2555.52kJ/kg(water)。從方程式(49)：
利用Δh/ΔW之半圓規，畫製Δh/ΔW=8555 kJ/kg(water)方向的參考線。繪製一條平行於參考線且經過狀態2的直線，這條線與15℃乾球溫度線的交點即為狀態1。因此，t1*=13.8℃。
一個在制定狀態線的替代（且相當正確）的方案，是利用半圖規的顯熱比尺規代替Δh/ΔW
尺規。ΔHs/ΔHt數值是空間內顯熱獲得量與總熱獲得量的比值。因此：
註解ΔHs/ΔHt=0.701在半圓規上相當接近Δh/ΔW=8555 kJ/kg(water)。
從方程式(47)或是(48)都可計算乾空氣的流量。從方程式(47)
在狀態1，v1=0.859 m3/kg(dry air)
因此，供應空氣的體積流率=mav1=0.856×0.849=0.735 m3/s
濕空氣之（熱、質）傳性質
特別是在熱傳的領域中，肯定地科學和實驗的工作，對濕空氣的許多其他性質是重要的。通常分類為傳遞性質，這些包括擴散係數(diffusion coefficient)、黏度(viscosity)、熱傳導係數(thermal conductivity)、及熱擴散因子(thermal diffusion factor)。Monchick (1965)用計算方式導出這些性質。表5及圖12及圖13是將作者成果的前三種性質列表概述。必須注意，在線圖1、2 和 3 的邊界之內， 在正常的大氣壓力下乾空氣的黏性很少變化， 並且熱傳導係數基本上是相同。
表5在101.325 kPa水—空氣之計算的擴散係數
Temp.,℃mm2/sTemp., ℃mm2 /sTemp., ℃mm2 /s
-7013.2022.25029.5
-5015.6522.95530.3
-4016.91023.66031.1
-3517.51524.37032.7
-3018.22025.110037.6
-2518.82525.813042.8
-2019.53026.516048.3
-1520.23527.319054.0
-1020.84028.022060.0
-521.54528.825066.3
空氣、水及蒸汽性質
Coefficient f w (or f s ) (over water) at pressures from 0.5 to 110 kPa for temperatures from 50 to 60℃(Smithsonian Institution).
Coefficient f i (over ice) at pressures from 0.5 to 110 kPa for temperatures from 0 to 100℃(Smithsonian Institution).
Compressibility factor of dry air at pressures from 0.001 to 10 MPa and at temperatures from 50 to 3000 K (Hilsenrath et al. 1960).
Compressibility factor of moist air at pressures from 0 to 10 MPa, at values of degree of saturation from 0 to 100, and for temperatures from 0 to 60℃ (Smithsonian Institution). [Note: At the time the Smithsonian Meteorological Tables were published, the value μ= W/Ws was known as relative humidity, in terms of a percentage. Since that time, there has been general agreement to designate the value m as degree of saturation, usually expressed as a decimal and sometimes as a percentage. See Goff (1949) for more recent data and formulations.]
Compressibility factor for steam at pressures from 0.001 to 30 MPa and at temperatures from 380 to 850 K (Hilsenrath et al. 1960).
Density, enthalpy, entropy, Prandtl number, specific heat, specific heat ratio, and viscosity of dry air (Hilsenrath et al. 1960).
Density, enthalpy, entropy, specific heat, viscosity, thermal conductivity, and free energy of steam (Hilsenrath et al. 1960).
Dry air. Thermodynamic properties over a wide range of temperature (Keenan and Kaye 1945).Enthalpy of saturated steam (Osborne et al. 1939).
Ideal-gas thermodynamic functions of dry air at temperatures from 10 to 3000 K (Hilsenrath et al. 1960).
Ideal-gas thermodynamic functions of steam at temperatures from 50 to 5000 K. Functions included are specific heat, enthalpy, free energy, and entropy (Hilsenrath et al. 1960).
Moist air properties from tabulated virial coefficients (Chaddock 1965).
Saturation humidity ratio over ice at pressures from 30 to 100 kPa and for temperatures from -88.8 to 0℃ (Smithsonian Institution).
Saturation humidity ratio over water at pressures from 6 to 105 kPa and for temperatures from -50 to 59℃ (Smithsonian Institution).
Saturation vapor pressure over water in millibars and for temperatures from -50 to 102℃ (Smithsonian Institution).
Speed of sound in dry air at pressures from 0.001 to 10 MPa for temperatures from 50 to 3000 K (Hilsenrath et al. 1960). At atmospheric pressure for temperatures from -90 to 60℃ (Smithsonian Institution).
Speed of sound in moist air. Relations using the formulation of Goff and Gratch and studies by Hardy et al. (1942) give methods for calculating this speed (Smithsonian Institution).
Steam tables covering the range from 0 to 800℃.
Transport properties of moist air. Diffusion coefficient, viscosity, thermal conductivity, and thermal diffusion factor of moist air are listed (Mason and Monchick 1965). The authors’ results are summarized in Table 5 and Figures 12 and 13.
Virial coefficients and other information for use with Goff and Gratch formulation (Goff 1949).
Volume of water in cubic metres for temperatures from -10 to 250℃ (Smithsonian Institution 1954).
Water properties. Includes properties of ordinary water substance for the gaseous, liquid, and solid phases (Dorsey 1940).
符號
α = ln(pw), parameter used in Equations (37) and (38)
μ = degree of saturation W/Ws, dimensionless
ρ = moist air density, kg3/m
ψ = relative humidity, dimensionless
C1 to C18= constants in Equations (5), (6), and (37)
dv =absolute humidity of moist air, mass of water per unit volume of mixture
D = enthalpy deviation, kJ/kg (dry air)
fs =enhancement factor, used in Equations (23a) and (25a)
h = enthalpy of moist air, kJ/kg (dry air)
ha =specific enthalpy of dry air, kJ/kg
has = hg- ha
hf= specific enthalpy of saturated liquid water
hfg= hg- hf= enthalpy of vaporization
hg =specific enthalpy of saturated water vapor
hs =enthalpy of moist air at saturation per unit mass of dry air
hs*=enthalpy of moist air at saturation at thermodynamic wet-bulb temperature per unit mass of dry air
hw =specific enthalpy of water (any phase) added to or removed from moist air in a process
hw*=specific enthalpy of condensed water (liquid or solid) at thermodynamic wet-bulb temperature and pressure of 101.325 kPa
Hs =rate of sensible heat gain for space
Ht= rate of total energy gain for space
ma =mass flow of dry air, per unit time
mw =mass flow of water (any phase), per unit time
Ma =mass of dry air in moist air sample
Mw =mass of water vapor in moist air sample
n = n + n, total number of moles in moist air sample
na =moles of dry air
nw =moles of water vapor
p = total pressure of moist air
pa =partial pressure of dry air
ps =vapor pressure of water in moist air at saturation. Differs from saturation pressure of pure water because of presence of air.
pw =partial pressure of water vapor in moist air
pws =pressure of saturated pure water
q = specific humidity of moist air, mass of water per unit mass of mixture
qs =rate of addition (or withdrawal) of sensible hea
R = universal gas constant,8314.41 J/(kg mole徬)
Ra =gas constant for dry air
Rw =gas constant for water vapor
s = entropy of moist air per unit mass of dry air
sa =specific entropy of dry air
sas = ss - sa
sf= specific entropy of saturated liquid water
sfg= sg - sf
sg =specific entropy of saturated water vapor
ss =specific entropy of moist air at saturation per unit mass of dry air
sw = specific entropy of condensed water (liquid or solid) at pressure of 101.325 kPa
t = dry-bulb temperature of moist air, ℃
td= dew-point temperature of moist air, ℃
t*= thermodynamic wet-bulb temperature of moist air, ℃
T = absolute temperature, K
v = volume of moist air, per unit mass of dry air
va =specific volume of dry air
vas = vs - va
vf = specific volume of saturated liquid water
vfg =vg- vf
vg =specific volume of saturated water vapor
vs =volume of moist air at saturation, per unit mass of dry air
vT= total gas volume
V = total volume of moist air sample
W = humidity ratio of moist air, mass of water per unit mass of dry air
Ws =humidity ratio of moist air at saturation
Ws*humidity ratio of moist air at saturation at thermodynamic wet-bulb temperature
xa =mole-fraction of dry air, moles of dry air per mole of mixture
xw =mole-fraction of water, moles per mole of mixtur
xws =mole-fraction of water vapor under saturated conditions, moles of vapor per mole of
saturated mixture
Z = altitude, m
參考文獻
Chaddock, J.B. 1965. Moist air properties from tabulated virial coefficients. Humidity and moisture measurement and control in science and industry. 3:273. Reinhold Publishing Corp., New York.
Dorsey, N.E. 1940. Properties of ordinary water substance. Reinhold Publishing Corp., New York.
Goff, J.A. 1949. Standardization of thermodynamic properties of moist air. Heating, Piping, and Air Conditioning 21(11):118.
Goff, J.A. and S. Gratch. 1945. Thermodynamic properties of moist air. ASHVE Transactions 1:125.
Goff, J.A., J.R. Anderson, and S. Gratch. 1943. Final values of the interaction constant for moist air. ASHVE Transactions 49:269.
Haines, R.W. 1961. How to construct high altitude psychrometric charts. Heating, Piping, and Air Conditioning 33(10):144.
Hardy, H.C., D. Telfair, and W.H. Pielemeier. 1942. The velocity of sound in air. Journal of the Acoustical Society of America 13:226.
Harrison, L.P. 1965. Fundamental concepts and definitions relating to humidity. In science and industry 3:289.
A. Wexler and W.H. Wildhack, eds. Reinhold Publishing Corp., New York.
Hilsenrath, J. et al. 1960. Tables of thermodynamic and transport properties of air, argon, carbon dioxide, carbon monoxide, hydrogen, nitrogen, oxygen, and steam. National Bureau of Standards. Circular 564, Pergamon Press, New York.
Hyland, R.W. and A. Wexler. 1983a. Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures to 5 MPa. ASHRAE Transactions 89(2A):520-35.
Hyland, R.W. and A. Wexler. 1983b. Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K. ASHRAE Transactions 89(2A):500-519
Karig, H.E. 1946. Psychrometric charts for high altitude calculations. Refrigerating Engineering 52(11):433.
Keenan, J.H. and J. Kaye. 1945. Gas tables. John Wiley and Sons, New York.
Kusuda, T. 1970. Algorithms for psychrometric calculations. NBS Publication BSS21 (January) for sale by Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.
Mason, E.A. and L. Monchick. 1965. Humidity and moisture measurement and control in science and industry.
Survey of the Equation of State and Transport Properties of Moist Gases 3:257. Reinhold Publishing Corp., New York.
NASA. 1976. U.S. Standard atmosphere, 1976. National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and the United States Air Force, Superintendent of Documents. U.S.
Government Printing Office, Washington, D.C.
NIST. 1990. Guidelines for realizing the international temperature scale of 1990 (ITS-90). NIST Technical Note
1265. National Institute of Technology and Standards, Gaithersburg, MD.
Osborne, N.S. 1939. Stimson and Ginnings. Thermal properties of saturated steam. Journal of Research,
National Bureau of Standards, 23(8):261.
Olivieri, J. 1996. Psychrometricsheory and practice. ASHRAE, Atlanta.
Palmatier, E.P. 1963. Construction of the normal temperature. ASHRAE psychrometric chart. ASHRAE Journal 5:55.
Peppers, V.W. 1988. Unpublished paper. Available from the ASHRAE Handbook editor.
Rohsenow, W.M. 1946. Psychrometric determination of absolute humidity at elevated pressures. Refrigerating
Engineering 51(5):423.
Smithsonian Institution. 1954. Smithsonian physical tables, 9th rev. ed. Available from the Smithsonian Institu
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Smithsonian Institution. Smithsonian meteorological table, 6th rev. ed. Out of print.
The international temperature scale of 1990 (ITS-90). Metrologia 27:3-10.
Threlkeld, J.L. 1970. Thermal environmental engineerin, 2nd ed. Prentice-Hall, New York, 175.
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