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Energy in Thermal Processes

Heat and Internal Energy

Internal energy U: associated with the

microscopic components of a system: kinetic and potential energies.

The larger the number of internal degrees of freedom of a system (translation, rotation or vibrations of molecules) the larger the internal energy.

Heat is the mechanism by which there is energy

transferred Q between a system and the environment because of a temperature gradient.

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Units of Heat

One calorie is the energy required to raise the

temperature of 1g of water from 14.5 0C to 15.5 0C

Units

Jcal 186.41 ≡

Specific Heat

The amount of energy per unit mass required to change the substance’s temperature by 1 0C. (It is an intrinsic property of each substance).

Tm

Qc

∆≡

Units

CkgJ 0/1

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Specific heat: questions

You have 1 kg of iron, 1 kg of glass and 1kg of water, all at 10 0C. Which of the three will be at highest temperature after 100 J of energy is transferred to each? Specific heat given in cal/g C.

a) Iron (0.107) b)glass (0.2) c) water (1.0)

The specific heat of A is larger than that of B and both are at temperature T. Mass of A is the same as mass of B. Which system will require more energy transferred by heat to double its temperature? a) A b) B c) both require the same?

Units of Heat: example

A diet doctor encourages people to diet by drinking ice water. His theory is that the body must burn off enough fat to raise the temperature of the water from 00C to 37.0 0C. How many liters of ice water would have to be consumed to burn off 454g of fat? (Assume that this amount of fat requires 3500 Kcal to be transferred to the ice. 1 liter= 1000cm3 and the density of water is 1.00 g/cm3).

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Calorimetry

The principle of energy conservation requires that the energy that leaves the warmer substance equals the energy that enters the colder one.

hotcold QQ −=

(Water is typically used for the cooling process)

)()( hhhccc TTcmTTcm −−=−

)(

)(

TTm

TTcmc

hh

ccch −

−=

How do we determine the specific heat of a substance?

Specific heat: example

Calculate the specific heat of a metal from the following data. A container made of a metal has mass 3.6 Kg and contains 14 Kg of water. A 1.8 Kg piece of the metal initially at a temperature of 180 0C is dropped in the water. The container and the water are initially at 16 0C. The final temperature of the whole system is 18 0C.

a) Neglect the change in temperature of the container.b) How does the result change when you account for the

change in temperature of the container?

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Latent heat and phase change

Sometimes a transfer of energy does not result in a temperature increase: it may go into different forms of internal energy (phase change).

mLQ ±=

Latent heat of fusion Lf is the energy required to melt (+) or freeze(-) one unit mass of the substance.

Latent heat of vaporization Lv is the energy required to boil (+) or condense (-) one unit mass of the substance.

Latent heat and phase change

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Latent heat: example

Consider the addition of energy to 1g of ice at –30 0C in a container held at constant pressure. Suppose that this energy results in the ice turning into steam at 1200C. The figure shows the experimental measurement of temperature as energy is added to the system. Explain the process and the energy quantities shown.

(cice=2090, cwater=4186, csteam=2010, Lf=3.33x105, Lv=2.26x10

6 all in SI)

Latent heat: example

A 150 g copper bowl contains 220 g of water, both at 20.00C. A very hot 300 g copper cylinder is dropped into the water causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 1000C. Specific heats in SI units are 4186 for water and 387 for copper. Latent heat of vaporization for water is 2.26 MJ/kg.

a) How much energy is transferred to the water?b) How much energy is transferred to the bowl?c) What was the original temperature of the cylinder?

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Energy transfer

Classification of Energy Transfer:

�Conduction�Convection

�Radiation

Thermal Conduction

A difference in temperature drives the flow of energy from a hot part of the system to the cold part.

the Rate of energy transfer is proportional to the cross-sectional area of the slab and the temperature difference, and inversely proportional to the thickness of the slab

L

TTAk

t

QP ch )( −=

∆≡

Thermal conductivity

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Thermal conductivities (k)

SI Units

mKW /1

Thermal conduction: home insultation

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Thermal conductivity

One can derive an expression for the rate of energy transfer through a compound slab:

∑

−=∆

=ii

ch

kL

TTA

t

QP

/

)(

∑

−=∆

=i

ch

R

TTA

t

QP

)(

In engineering the term L/k is usually referred to a R-value of the material (resistance to thermal conduction)

Resistance to thermal conduction (R)

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Thermal conduction: questions

Materials having high thermal conductivity provide better insulation than materials having low thermal conductivity.

a) True b) false

The thermal resistance of wall A is larger than that of wall B. Which of the following statements is correct:

a) Wall A is best at insulating the house because it allows for larger energy transfer rate

b) Wall A is best at insulating the house because it reduced the energy transfer rate

c) Wall B is best at insulating the house because it allows for larger energy transfer rate

d) Wall B is best at insulating the house because it reduces the energy transfer rate

Thermal conduction: questions

A board of length L and thermal conductivity k is used to insulate one wall. Another board of length 2L and thermal conductivity 2k, is used to insulate another wall of the area in the same house. In which wall is the rate of energy transfer larger?

a) The first b)the latter c) both the same

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Thermal conduction: example

a) Calculate the rate at which body heat is conducted through the clothing of a skier in a steady-state process, given the following data: the body surface area is 1.8 m2

and the clothing is 1.0 cm thick; the skin surface temperature is 330C, whereas the outer surface of the clothing is at 1.00C; the thermal conductivity of the clothing is 0.040 W/m K.

b) How would the answer a) change if the skier’s clothes became soaked with water of thermal conductivity 0.60 W/mK?

Convection

Energy transfer by the movement of the substance is referred to as convection.

Natural convection results from a flow due to differences in densities

Forced convectionhappens when a fan or a pump force the motion of hot air or hot water in heating systems

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Thermal processes: questions

A house has an electric heating system uniquely based on heating pads placed on a black ceiling. Why is this system not effective?

a) Because one cannot reach the ceilingb) Because natural convection does not move the air aroundc) Because a black ceiling does not radiate

Radiation

All objects radiate energy continously in form of electromagnetic waves (ex: light). The rate at which an object radiates energy is known as Stephan’s Law

P = power in Wattss= constant (5.669x10-8 W/m2K4)

A= surface areae=emissivity (varies from 0 to 1)T= temperature (in Kelvin!)

4AeTP σ=

e=1 ideal absorber(black body)

e=0 ideal reflector

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Radiation

Any object at a temperature T(obj) radiates energy but also absorbs energy from its surroundings at a temperature T(ext). The net effect will be

When an object is in thermal equilibrium the rate at which is radiates equals the rate at which it absorbs energy. So the net rate is zero and it’s temperature remains constant.

)( 44extobjnet TTAeP −= σ

Radiation: questions

Stars A and B have the same radius and emissivity. Star A has twice the absolute temperature of star B. What is the ratio of star A’s power output to star B’s power output due to radiation?

a) 2 b) 4 c) 8 d) 16

Stars A and B have the same temperature and emissivity, but star A has twice the radius of star B. What is the ratio of star A’s power output to star B’s power output due to radiation?

a) 2 b) 4 c) 8 d) 16

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Radiation: example

A sphere of radius 0.500 m, temperature 27.00C and emissivity 0.850 is located in an environment of temperature 77.00C. At what rate does the sphere

a) emit thermal radiation?b) absorb thermal radiation?c) what is the net rate of energy exchange?

Resisting energy transfer

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Global warming