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ThermodynamicsChapter 3

Properties of a Pure Substance

國立成功大學工程科學系

Properties and the behavior of substances are veryimportant for our studies of devices andthermodynamic systems (see figures in chap. 1)

We’ve studied 3 familiar properties of a substance –V ( ), P and T. We now turn to pure substances and consider some of the phases in which a pure substance may exist, the number of independent properties of it, and methods of presenting thermodynamic properties.


The Pure Substance


3.1

A pure substance: One that has a homogeneous and invariable chemical composition.

Simple compressible substance: substance whose surface effect, magnetic effect, and electrical effects due to external force fields are insignificant.


Vapor – Liquid – Solid – Phase Equilibrium in a Pure Substance

(Phase – Change process of Pure Substances)(Property Diagrams for Phase-Change Processes)


3.2


Figure 3.1 Constant-pressure change from liquid to vapor phase for a pure substance.

saturation temperature: the temperature at which vaporization takes place at a given pressure, and the pressure is called saturation pressure of the given temperature.

vapor – pressure curve (liquid-vapor saturation curve): For a pure substance, there is a definite relation between saturation pressure and saturation temperature.

For water at 0.1MPa, the saturation temp is 99.6 .For water at 99.6 the saturation pressure is 0.1MPa.


Figure 3.2 Vapor-pressure curve of a pure substance.


Saturated liquid: liquid at the saturation temperature and pressure.

Subcooled liquid: liquid temp<saturated temp for the given pressure.

Compressed liquid: liquid press > saturated press for the given temperature.

When a substance exists as part liquid and part vapor at the saturation temp. its quality ( ) is defined as the ratio of the mass of vapor to the total mass. is an intensive property, and exists only in a saturated state.


Saturated vapor ( =100%): vapor at the saturated temperature.

Super heated vapor (i.e. gas): vapor temp. > saturated temp.

States between saturated liquid and saturated vapor are saturated liquid-vapor mixtures


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學生上課專心(用心)聽講與看text才能

了解 e.g.“saturation temperature”與“saturation pressure” 真的(相信)否?

Q:一瓶裝水喝1/4後蓋上，它的內部有water vapor嗎? WHY?

A:

其內有water vapor. e.g.可將之置入冰箱中可見其內有凝固的水滴可證實之。

Q:為何其瓶內有water vapor? Why?

你可以 saturation temperature or saturation pressure 解釋嗎? 你了解它們?

A phase (P-T) diagram is useful in understanding the change of states of a substance along a (const-P, -T, -V) process.

See the powerpoint #24

students pay attention in class and read text then.

What, if “ice” in the bottle instead of the “water” for that question?

Discuss it according to (a) room temp and (b) say, -10 C.

The variations of properties during phase-change processes are best studied and understood with the use of property diagrams.

For examples: T- , P- , and P-T diagramsof pure substances.


Figure 3.3 Temperature-volume diagram for water showing liquid and vapor phases (not to scale).


As the pressure of the constant-pressurephase-change process increase, the phase-change horizontal line, connecting thesaturated liquid and saturated vapor, becomesmuch shorter. It continues to shrink as thepressure further increase until point N (pointof inflection with a zero slope, 22.09 MPa374.14 ) is reached ,


where there is no constant-temperaturevaporization process. This point is called thecritical point, where the saturated-liquid andsaturated-vapor state are identical. The critical-poin t thermodynamic data are givenin Tables A.2 & 3.1.


Saturated liquid-vapor homogeneous mixtureThe total volume (mass) is the sum of the liquid volume (mass) and the vapor volume (mass).

Now, define

Equation 3.1 become

Thus, can be viewed as the distance between saturated liquid and saturated vapor.


Figure 3.4 T-v diagram for the two-phase, liquid-vapor region to show the quality specific volume relation.


Extending the T- (or P- ) (liquid-vapor) diagrams to include solid phases. Read Section 3.2

Read P. 43 ice → water, saturated solid (ice) , < ….. (unusual) Recall: the const-P process!

Sublimation: transition from the solid phase directly into the vapor phase.

Triple point: the state in which all three phases coexist in equilibrium.

On T- or P- diagrams, these triple-phase states form a line (why?) called triple-lines. It, however, appears as a point on the P-T diagram, and is called the triple point.


v

Figure 3.5 shows the P-T diagram of a pure substance ( ). This diagram is called the phase-diagram since all 3 phases are separated from each other by the 3 lines.


A phase (P-T) diagram is useful in understanding the change of states of a substance along a (const-P, -T, -V) process.

Does it provide answers to the water bottle question asked last week?

Figure 3.5 Pressure-temperature diagram for a substance such as water.


Most comments so far for , all pure substances exhibit the same general behavior of vapor-liquid-solid-phase equilibrium processes.

However, the triple-point temperature and critical temp. vary greatly from one substance to another.


For example, the critical temp. of helium is 5.3K (<< 300K)

the critical temp. of is 647K (~ 2倍室溫)

Most metals have a much higher critical temp. than .

Sublimation occurs because the pressure below the triple-point value.

Therefore, it is helpful to think of a given state of a substance in relation to the critical state or triple point.


Figure 3.6 Carbon dioxide phase diagram.


Figure 3.7 Water phase diagram.

A pure substance can have a number of triple points, but only one triple point has a solid, liquid, and vapor equilibrium. Others are, for example, 2 solid phases and 1 liquid phase, 2 solid phases and a vapor phase, or three solid phases.

Allotropic transformation: A transition from one solid phase to another.


Remarks:

One usually experiences a change of the state (phase) of water under the const-P process. One needs to discuss it according to P > or < P (triple-point).

Do you experience this water under a const-T process? One then needs to discuss it according to T > or < T (triple-point).

It, therefore, is important to understand what processes in a given problem.

Independent Properties of a Pure Substance


3.3

One important reason for introducing the concept of a pure substance is that the state of a simple compressible pure substance is determined (defined) by two independent properties.

Note that the temperature and pressure are not independent properties for a saturated state.

The state of air, which is a mixture of different gases of definite composition, is determined by specifying 2 properties if it remains in the gaseous phase. Air then can be treated as a pure substance.


Tables of Thermodynamic Properties


3.4

Tables of thermodynamic properties of many substances ore available, and in general, all have the same form. We refer to the steam tables in this section. The steam tables in Appendix B consists of five separate tables.

Figure 3.8 Listing of the steam tables.國立成功大學工程科學系

Table B.14 gives the properties of the compressed liquid. Consider a piston and a cylinder (Fig. 3.9) contains 1 Kg of saturated liquid at 100 , P = 0.1013 MPa, = 0.001044 /Kg from Table B.1.1.


Now, increase the pressure to 10 MPa while Temp. still at 100 by a necessary heat transfer Q. Table B.1.4 gives

= 0.001039 /Kg, OK! However, obtained from saturated liquid at 10 MPa (when T = 311.1 ) is = 0.001452 /Kg, which is 40% in error!

Remarks: One may assume the of a compressed liquid = that

of the saturated liquid at the same temp. However, it is not a good approximation to assume the of a compressed liquid = that of the saturated liquid at the given (or same) pressure.



Figure 3.10 Diagram for Example 3.1.


Figure 3.13 A T-v diagram for water at 300kPa.

Figure 3.14 T and v values for superheated vapor water at 300kPa.

(Carefully) read Examples 3.1 – 3.7,e.g. the remarks in Ex. 3.3 (p. 50),

Also read e.g. “How do I find a state in the B-section tables? ” in 3.10 How-To Section in p. 65.

Thermodynamic Surfaces


3.5

The variation of properties during phase-change processes (or P- -T behavior of a pure substance) discussed so far can be well summarized by a consideration of a pressure-specific volume-temperature (P--T) surface.


Fig3.18: P- -T surface of a substance that expands on freezing.

Fig3.19: P- -T surface of a substance that contracts on freezing.

∵A pure substance has only 2 independent intensive properties.

∴Each possible eq’m state is represented by a point on the surface.


Figure 3.18 Pressure-volume-temperature surface for a substance that expands on freezing.


Figure 3.19 Pressure-volume-temperature surface for a substance that contracts on freezing.


These two P – – T surfaces areP = P (T , )

The single-phase regions are curved surfaces on the P- -T surface.

The two-phase regions (i.e. phase-change processes) are surfaces perpendicular to the P-T plane.


Various lines of constant temp. are shown on the P – diagrams, and the corresponding constant – temp. sections on the P – – T surfaces are lettered identically.

Students read p. 54-55

先熟悉(了解)水於T- (Fig3.3), P- 與P-T(Fig3.4)平面上顯示其液態、飽合液態、液-氣雙相狀態、飽合氣態與氣態的圖。然後下課後問自己看懂Fig3.18與Fig3.19

嗎?分別知道其圖上之液態、固態在何處？自vapor沿著等溫線隨壓力增大至液+固(或固+液)雙相區時，是先經過液相或固相?

Discuss this in terms of T > or < T

(Triple point).

For a substance expanding on freezing (Fig. 3.18, T < T (triple point)), its freezing temperature decreases as pressure increases.

For a substance contracting on freezing (Fig. 3.19, T > T (triple point)), its freezing temperature increases as pressure increases.

Q: Why various lines of constant temperature are shown in P- -T diagram? in P- or even T-diagrams?

Let’s examine the following processes(in Figs 3.18 and 3.19)

As the pressure of vapor is increased along the const-temp lines abcdef in Figs. 3.18 and 3.19, respectively, it (a substance that expands on freezing) first become solid and then liquid; however it (a substance that contracts on freezing) first become liquid and then solid.Why?

Hints (recall): in two-phase regions, lines of constant pressure are also lines of constant temperature; in phase-change processes, temperature remains unchanged as the specific volume increases significantly for a given pressure; the projections of two-phase regions on the P-T plane are lines (recall the phase diagram Fig.3.5)


The P-V-T behavior of low andmoderate-density gases


3.6

Property tables provide accurate information, but they are bulky and vulnerable to typographical errors. Any equation that relates the pressure, temp, and specific volume of a substance is called an equate of state.

It has been observed experimentally that, to a close degree, a low-density gas behaves according to the ideal gas equation of state


, the number of Kmol of gas (3.4)

is the universal gas constant

T is the absolute temp. in Kelvins


Q: Over what range of density will the ideal-gas eq. of state is a good approximation ? and how much does an actual gas at a given press and temp. deviate from ideal-gas behavior ?



Figure 3.21 Temperature-specific volume diagram for water.

The Compressibility Factor, Z


3.7

Thus, the deviation of Z from unity is a measure of the deviation of the actual relation from the ideal-gas eq. of state.



Figure 3.22 Compressibility of nitrogen.

Observations:part (I)

1. Z → 1 as P → 02. T > 300 K, for Press. up to 10 MPa3. Z deviates from unity for very high

press. and low temp.


Part (II)

4. Compressibility diagrams of other substancesare similar in a qualitative sense.

5. What exactly constitutes low pressure or high temp.? Is – 100 a low temp.? It is for most substances but not for air or . They can be treated as an ideal-gas at this temp. and atmospheric press. with an error of 1%, because is well over its critical temp. (-147 ).


Therefore, the temp. or press. of a substance is high or low relative to its critical temp. or press.

Q: Is there a way in which we can treat other substances on a common basis, such as Fig. 3.22 ?


Is it possible to model non-ideal-gases still using this concept of the compressibility factor along with a dimensionless generalized compressibility chart for most gases ?

A, YES! next three pages.


Gases behave differently at a given temperature and pressure, but they behave very much the same at temperatures and pressures normalized with respect to their critical temperatures and pressures. The normalization is done as


The Z factor for all gases is approximately the same at the same reduced pressure and temperature. This is called the principle of corresponding states. In Fig.3-51(given in class), the experimentally determined Z values are plotted against and for several gases.


The gases seem to obey the principle of corresponding states reasonably well. By curve-fitting all data, we obtain the generalized compressibility chart, Fig.D1, that can be used for all gases.


The following observations can be made from the generalized compressibility chart:

At very low pressure ( << 1), gases behave as an ideal gas regardless of temperature.

At high temperature ( > 2), ideal-gas behavior can be assumed with good accuracy regardless of pressure (except when >> 1 ).

The deviation of a gas from ideal-gas behavior is greatest in the vicinity of the critical point.


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