14 Heat

• Homework:

• Problems: 3, 5, 13, 21, 33, 47, 49.

• Internal Energy

• Heat Capacity & Specific Heat

• Phase Transitions

• Thermal Conduction

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2

Heat

• Heat is energy transferred due to temperature difference.

• Symbol, Q [J]

• Ex. 4186J heat needed to raise 1kg of water one degree C.

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example c’s

• in J/(kg·°C)

• aluminum 920

• copper 390

• ice 2100

• water 4186

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• c = Q/mT [J/(kg·K)]• heat to raise 1kg by 1 degree °C or K. • slope warming curve = T/Q = 1/(mc)• Q = mcT

specific heat

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Calorimetry• Measure heat lost/gained:

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Example Calorimetry

• 2kg of “substance-A” heated to 100C. Placed in 5kg of water at 20C. After five minutes the water temp. is 25C.

• heat lost by substance = heat gained water.

wA QQ

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continued:

wwwAAA TcmTcm

)2025)()(5()25100)()(2( CCckgCCckg wA

wA QQ

))(25())(150( wA cCkgcCkg

Ckg

Jcc wA

6986

4186)(

6

1)(

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• L = Q/m [J/(kg)]

• heat needed to melt (f) or vaporize (v) 1kg

Phase Transitions: Latent Heat

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example L’s

• in J/kg:

• melting (f) vaporization (v)

• alcohol 100,000 850,000

• water 333,000 2,226,000

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Example:

• How much heat must be added to 0.5kg of ice at 0C to melt it?

• Q = mL = (0.5kg)(333,000J/kg)

• = 167,000J

• same amount of heat must be removed from 0.5kg water at 0C to freeze it.

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Heat Transfer

• Conduction

• Convection

• Radiation

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Conduction

• Heat conduction is the transmission of heat through matter.

• dense substances are usually better conductors

• most metals are excellent conductors

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conduction equation

• heat current = energy/time [watts]

• heat current = kAT/L

• k = thermal conductivity

• & T = temperature difference, L below

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conduction example• some conductivities in J/(m-s-C°):

• silver 429 copper 401 aluminum 240

• Ex: Water in aluminum pot. bottom = 101°C, inside = 100°C, thickness = 3mm, area = 280sq.cm.

• Q/t = kA(Th-Tc)/L

• = (240)(0.028)(101-100)/(0.003)

• = 2,240 watts heat current

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Heat transfer

• 2m x 1m window, 4mm thick, single pane glass.

• Assume temp. difference = 5°C

• Q/t = kA(T)/L = (0.84)(2)(5)/0.004

• About 2,000 watts

R-Factors and Thermal Resistance

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units] SIin quoted[not factor-Rd

[K/W] R resistance thermalA

d

factor-R Current Heat

TA

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Convection

• Convection – transfer through bulk motion of a fluid.

• Natural, e.g. warm air rises, cool falls

• Forced, e.g. water-cooled engine

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Radiation

• Heat transfer by electromagnetic radiation, e.g. infrared.

• Examples:• space heaters with the shiny reflector use

radiation to heat. • If they add a fan, they use both radiation and

convection

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Summary

•Definition of Internal Energy

•Heat Capacity

•Specific Heat

•Phase Transitions

•Latent Heat

•Phase Diagrams

•Energy Transport by Conduction, Convection, and Radiation

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Example:

• A student wants to check “c” for an unknown substance. She adds 230J of heat to 0.50kg of the substance. The temperature rises 4.0K.

Kkg

J

Kkg

J

Tm

Qc

115

)0.4)(5.0(

230

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Greenhouse Effect

• ‘dirtier’ air must be at higher temperature to radiate out as much as Earth receives

• higher temperature air is associated with higher surface temperatures, thus the term ‘global warming’

• very complicated model!

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Phase Change

• freeze (liquid to solid)

• melt (solid to liquid)

• evaporate (liquid to gas)

• sublime (solid to gas)

• phase changes occur at constant temperature

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Temperature vs. Heat (ice, water, water vapor)

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Heat and Phase Change

• Latent Heat of Fusion – heat supplied to melt or the heat removed to freeze

• Latent Heat of Vaporization – heat supplied to vaporize or heat removed to liquify.

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Newton’s Law of Cooling

• For a body cooling in a draft (i.e., by forced convection), the rate of heat loss is proportional to the difference in temperatures between the body and its surroundings

• rate of heat-loss ~ T

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Real Greenhouse

• covering allows sunlight to enter, which warms the ground and air inside the greenhouse.

• the ‘house’ is mostly enclosed so the warm air cannot leave, thus keeping the greenhouse warm (a car in the sun does this very effectively!)

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Solar Power

Solar Constant• Describes the Solar Radiation that falls on an

area above the atmosphere = 1.37 kW / m².

In space, solar radiation is practically constant; on earth it varies with the time of day and year as well as with the latitude and weather. The maximum value on earth is between 0.8 and 1.0 kW / m².

• see: solarserver.de