1. Environmental Physics
Chapter 4:
Heat
Copyright © 2008 by DBS

2. Introduction
~20% of all the energy in US is used for heating and cooling buildings
Residential sector uses 50% for space heating
Energy (conservation) efficiency should be first step in dealing with environmental impacts…
Figure 4.1: U.S. household energy consumption by end use. 1 Quad = 1015 Btu.

3. Introduction
Thermodynamics – study of heat and work

4. Heat and Work and the First Law
Total Energy, E:
E = KE + PE + TE + chemical energy + electrical energy
Heat (Q) and work (W) are the only ways to add energy to an object to change its total E, 1st law of thermodynamics:
Won+ Qto = Δ(KE + PE + TE + chemical energy + electrical energy) = ΔE
Law of Conservation of Energy: The work done on a system plus the heat added to it is equal to the change in the total energy of that system
or Energyin = Energyout

5. Heat and Work and the First Law
Important discovery of the 18th century: heat is the transfer of energy between two bodies due to temperature differences
Previously, heat was mistakenly thought to be a material fluid, called “caloric” that would flow from a hot body into a cold one, causing an increase in temperature and mass
British physicist James Joule, in a series of highly accurate experiments, provided conclusive evidence that heat is a form of energy in transit and that it can cause the same changes in a body as work

6. Heat and Work and the First Law
Equivalence between mechanical work and heat
Joule measured the increase in temperature of a water bath when a paddle wheel was turned
Observed the same effect (rise in water temperature) either with the performance of work or by addition of heat
Units are Joules or ft.lbs (heat is a form of Energy)
Figure 4.2: Relationship between work and heat. A temperature change in the water can be caused either by letting the weight drop (causing the blades to rotate) or by adding heat from the gas burner.

7. Heat and Work and the First Law
Work done on a system = -ve of work done by the fluid
Won = - Wby
Qto= ΔE + Wby
Heat added to a system is equal to the change in the total energy plus the work Wby done by the system
e.g. sun heats a balloon, temperature increases (TE inc.) and balloon expands doing work on the surrounding
e.g. bicycle pump is pushed down, work is done on the system, resulting in increasing the air’s temperature
Figure 4.3: Bicycle pump. Work done on the air in pushing the handle down results in an increase in the air’s thermal energy. W = F × d = ΔTE.

8. Temperature and Heat Temperature
Property of an object, much like color and shape
measurement of average KE of molecules
Cannot tell us the amount of energy in a substance, since it is independent of mass
Heat can be converted into other forms of energy such as motion or electricity.

9. Temperature and Heat
Because the temperature scales have different zero points, formulas must be used to carry out the conversions
K = ºC
ºC = K
Melting point ice 9
(ºC)
+ 32 or
ºF=
1.8(ºC) + 32 5
ºC = 5
(ºF - 32) or
(ºF - 32) 9
1.8

10. Farenheit, Celcius and Kelvin Scales
Melting point ice

11. Example Temperature Conversions
1. Convert 350 oF to oC and K
oC = ( )(5/9) = (318)(5/9) = 177 oC
K = = 450 K
2. Convert -40 oC to oF
oF = (9/5)(-40) + 32 = 9(-8) + 32 =
= - 40o F
3. Convert 298 K to oC
oC = = 25 oC

12. Temperature and Heat Heat
measure of total energy content of vibrating molecules (KE and PE)
can tell us the amount of energy in a substance, since it is dependent on mass
governed by law conservation of energy – Joule’s exp.
Heat is energy that flows from one object to another when there is a difference in temperature between the objects
Temperature determines the direction of heat flow
hotter → cooler object
Heat can be converted into other forms of energy such as motion or electricity.

13. Heat and Temperature
objects can have the same temperature but different amounts of heat
Figure 4.4: Thermal energy. (a) If both brick assemblies are heated in a kiln for several hours, they will have the same temperature, but the larger array will store nine times as much thermal energy as the smaller one.
Steam burn – temp. is equal but heat content is greater

14. Temperature and Heat Specific heat capacity (c)
When heat is added to a substance, we usually find an increase in temperature
heat energy (joules) required to raise 1 g of a substance up by 1 °C (or 1 K)
different substances require different amounts of heat
Large c of water makes it an excellent coolant
substances with small specific heats absorb little energy when warming and give off little energy when cooled
Why is c for H2O so much more than Cu?

15. Heat and Temperature Heat Capacity
When the samples are both heated by 1 °C, the addition to the KE (motion of molecules) is the same
For water, more energy must be added to the PE (energy from intermolecular forces) part of internal energy

16. Temperature and Heat What factors are important? Mass (m)
Temperature change, T = Tf –Ti
I.D. of substance, steel, water, (specific heat capacity, c)
Heat gained or lost,
Q = mcT
Iron’s ability to store heat is less than waters

17. Question
What is more effective in cooling your cup of coffee, 100 g aluminum or 100 g milk?
Aluminum has lower c than milk (which is mostly water). The aluminum absorbs less heat from the coffee for each degree of temperature that it changes than the milk does.

18. Question
Calculate the heat energy required to raise the temperature of 24.5 g of mercury from 5.0 oC to 35.2 oC
T = = 30.2
m = 24.5 g
c = 0.14 kJ
kg K
Q = mcT
Q = (0.14 kJ) ( kg) (30.2 K ) = 0.10 kJ

19. Question
A kettle full of water is rated at 2 kW and starting at room temperature (25 ºC) takes 4 minutes to boil.
(i) How much energy is used?
(ii) How much water was boiled?
2 kW = 2 kJ / s
E = Pt = 2 kJ / s x 240 s = 480 kJ
Q = mcT
Q = 480 kJ = (m) (4.2 kJ ) (75 K )
kg K
 m = 1.5 kg

20. Specific Heat Capacity
Question
Which object experiences the greatest temperature change?
Assume equal masses and heat losses.
Substance
Specific Heat Capacity
Marble
0.88
Aluminum
0.91
Copper
0.380
Copper will have the largest temperature change
ΔT = Q mc

21. Temperature and Heat
Adding heat may not increase the temperature!
May change state of matter
At the boiling / melting temperature, adding heat energy changes state WITHOUT RAISING THE TEMPERATURE

22. Temperature and Heat Latent Heat
Latent heat = energy needed to change state (solid, liquid, gas) without affecting temperature
e.g. Energy needed to evaporate water is released when water condenses
e.g. Energy needed to melt ice is released when water freezes
Sensible heat = heat that results in temperature change
Substance
Latent heat fusion
(kJ / kg)
Latent heat evaporation (kJ / kg)
Water
335
2260
Lead 23
858
Aluminum
393
10,500
Latent heats are high compared with specific heat capacity – intermolecular bonds must be broken
Q = m Lf

23. Question
How much thermal energy in joules must be absorbed by 50 g of ice at 0 ºC to melt it?
Q = m Lf
= kg x 334 kJ/kg = J
How much thermal energy will be released when 50 g of water freezes?
16700 J

24. Temperature and Heat Heat liberated Heat absorbed
Heat absorbed
At the boiling / melting temperature, adding heat energy changes state WITHOUT RAISING THE TEMPERATURE

25. Question
If the specific heat capacity of ice is 2.1 kJ kg-1 K-1, how much heat would have to be added to 200 g of ice, initially at -10 °C to raise the ice to the melting point and completely melt the ice?
Total energy = Qraise + Qmelt
Total energy = mc T + m Lf
= (0.200 kg x 2.1 kJ kg-1 K-1 x 10 K) + (0.200 x 334 kJ kg-1)
= 4.2 kJ kJ = 71 kJ

26. End
Review

27. Heat Transfer Principles
Figure 4.7: Heat flows when there is a temperature difference ΔT. In this case, ΔT = 70° − 50° = 20°F
Heat Transfer
One of two ways in which energy can be transferred to a body
Occurs when there is a temperature difference
Occurs through conduction, convection and/or radiation

28. Heat Transfer Principles Conduction
Conduction – movement of heat through a solid substance, exchange of thermal energy between atoms
Most important in solids
Block demonstration
Fourier’s Law
Figure 4.8: Heat is transferred by conduction through the metal spoon from the hot coffee to the colder fingers.

29. Demo Why does B melt the ice quicker than the warm block?
Metal conducts heat more readily than wood, so more heat flows from your hand into the metal than the wood. Since contact with the metal cools your hand more rapidly the metal block feels colder.

30. Heat Transfer Principles Conduction
Depends on temperature gradient, size of conductor and conductivity
Rate of heat transfer by conduction (Qc/t)
Where Q = heat (J) transferred in time t (s), k = thermal conductivity (W m-1 K-1), A = surface area, δ = thickness, T1 and T2 are temperatures on each side
Fourier’s Law

31. Heat Transfer Principles Conduction
Rate of heat transfer by conduction (Qc/t)
Q = kA(T2 – T1)
t δ
Good insulators e.g. polystyrene, wool jumpers rely on incorporating air into structure
Substance
Thermal Conductivity
W m-1 K-1
Diamond
1000
Copper
401
Aluminum
210
Iron 76
Glass
1.1
Brick
0.13
Water
0.62
Air
0.024
Fourier’s Law

32. Heat Transfer Principles Conduction
Rate of heat transfer by conduction (Qc/t)
Q = kA(T2 – T1)
t δ
To reduce heat loss:
Reduce T2
Reduce A
Increase δ
Fourier’s Law
Figure 4.10: Percentage of energy saved by lowering the thermostat from 72°F to the values shown on the curved lines, for the time periods shown.

33. Heat Transfer Principles Convection
Gases and fluids molecules are too far apart for heat to conduct
Figure 4.11: Convection currents in water.

34. Heat Transfer Principles Convection

35. Demo
Galilean thermometer
Liquids change density when heated

36. Transmission of Heat Convection
Warm fluid expands, density decreases and it tends to rise
Ocean currents and winds redistribute heat from the tropics to the poles

37. Heat Transfer Principles Convection
May be natural (density differences) or assisted by wind
Figure 4.12: Heat transfer through a double-pane window.

38. Heat Transfer Principles Convection
Convection currents are important in some types of solar heating systems
Figure 4.13: Solar air heater for use in a window.

39. Transmission of Heat Radiation
EM radiation is transferred not through matter, but through electrical and magnetic fields
Self propagating as it moves through space
Electrical charges are accelerated
Carries energy and momentum which may be imparted on interaction with matter
does not require a medium in which to travel

40. Transmission of Heat Radiation
3 Hz
Classified according to frequency
v = f λ
Where:
v = speed of light = 3 x 108 (m/s), f = frequency (Hz or cycles s-1), λ = wavelength (m)
Different types of EM radiation all have the same velocity in a vacuum
3.0 x 108 m/s = 1.1 billion km/h = 671 million mph
1 Hz

41. Question
What is the wavelength of a cell phone using the microwave frequency (GHz)?
f x λ = 3.0 x 108
λ = 3.0 x 108 /109 = 0.3 m

42. Figure 4.15: The electromagnetic spectrum, shown as a function of wavelength.
Fig. 4-15, p. 112

44. Transmission of Heat Radiation
All objects above absolute zero (0 K) emit radiation
Amount of energy emitted from an object is proportional to its temperature
Humans, animals, the Earth etc. and basically anything < 1000 °C emit IR
Sun’s surface ~ 6000 °C emits primarily visible radiation + some IR and UV
cf.
Earth emits majority long-wave (LW) radiation = Infra-red
Sun emits majority short-wave (SW) radiation = visible
Stefan-Boltzman and Wien’s laws

45. Transmission of Heat Radiation
For a body to maintain a certain temperature, Energyin=Energyout
At night a body continues to radiate heat – radiative cooling
Figure 4.17: The equilibrium temperature of an object is maintained if the energy input is equal to the energy output.

46. Convection – movement of heat through a fluid (liquids and gases) brought about by changes in temperature affecting density
Conduction – movement of heat through a solid substance, exchange of thermal energy between atoms
Radiation – transfer of heat energy via electro-magnetic waves through a vacuum
Figure 4.18: A hot-water radiator as an illustration of heat transfer via conduction, convection, and radiation.
Figure 4.18: A hot-water radiator as an illustration of heat transfer via conduction, convection, and radiation.
Fig. 4-18, p. 115

47. End
Review

48. Heat Engines
“heat engines” – devices in which heat is converted into useful work
e.g. automobile, electrical generating plant
Requires a source of heat, e.g. burning a fuel, nuclear, solar etc.
The flow of heat proceeds through the “working fluid” (gas or liquid)

49. Heat Engines Energy flow diagram for a heat engine:
Since energy is conserved heat leaving the source (QH) is equal to the heat entering the sink (QC) plus work done (W)
QH = QC + W
and W = QH - QC
Higher TH and lower TC the higher the work output
Energy available for work comes from a decrease in the total energy of the working fluid
Figure 4.19: A heat engine transforms heat into work.

50. Heat Engines Open cycle – working fluid is exhausted into environment
e.g. 4-stroke gasoline
Intake
Compression
Power (volume expansion of gas)
Exhaust

51. Heat Engines
Closed cycle – working fluid is sent back to the heat source to start the cycle over
e.g. steam turbine – working fluid = water
QH = W + QC
Heat into plant = net work out + net heat out (fuel combustion) (electricity) (of condenser)
W comes from dec. in ΔE of the steam, condenser provides low-temp. sink

52. Heat Engines Types of heat engines: Working fluid changes state
Working fluid remains a gas (air)

53. Heat Engines Ocean Thermal Conversion (OTEC)
Figure 4.20: Ocean Thermal Energy Conversion (OTEC). The temperature difference between waters on the top of the water and down deep allows one to construct a heat engine.

54. The Second Law of Thermodynamics
Why doesn’t book lying on a table take thermal energy from the table and convert it into kinetic energy (work)?
1st law of thermodynamics doesn’t prevent this form happening!
Figure 4.21: Impossibilities according to the second law of thermodynamics. (a) Heat withdrawn from the table is converted into mechanical energy—the kinetic energy of the block, (b) Heat from sea water is converted into electrical energy (the resulting ice cubes are discarded).

55. The Second Law of Thermodynamics
Second law of thermodynamics: for any spontaneous process, the entropy (disorder) of an isolated system can only increase or stay the same, but never decrease
Important statements that follow from the second law:
Heat can flow spontaneously only from a hot source to a cold source
No heat engine can be constructed in which heat from a hot source is converted entirely to work. Some heat has to be discharge to a sink at a lower temperature (cf. previous examples)

56. The Second Law of Thermodynamics
The efficiency (η) of an energy conversion process is defined as:
η = Eout/Ein x 100 %
Principle of conservation of energy says that the work output (energy out) equals the heat input minus the heat transferred out (W = QH – QC):
Efficiency = W = QH – QC x 100%
QH QH
= 1 – (QC / QH) x 100%
If some heat is transferred out to a cold sink, then we can never have a 100% efficient process
Therefore we will never have perpetual motion machines…

57. The Second law of Thermodynamics Maximum Efficiency
If some heat has to be discarded, what is the best we can do?

58. The Second law of Thermodynamics Maximum Efficiency
Upper temperature limit is 500 ºC (restricted by engineering, pollution and corrosion), exhaust temperature 100 º C
Max possible efficiency for a heat engine (Carnot efficiency):
η = TH – TC x100 % = 1 – TC/TH x100 % TH
η = 61% (must be computed in K)
Theoretical upper limit, other losses (e.g. friction, heat loss from boilers, transmission losses)
At best we can convert 35 % of the thermal energy in burning fossil fuels to mechanical/electrical
More than ½ lost as waste heat

59. Question
A heat engine takes in 1200 J of heat from the high temperature heat source in each cycle and does 400 J of work in each cycle. What is the efficiency of the engine? How much heat is released to the environment in each cycle?
η = W/QH = 400 J / 1200 J = 33%
From 1st law: W = QH - QC = 1200 J - QC = 400 J
QC = 800 J

60. Question
Calculate the efficiency of a power station located in a colder climate (Tc = 0 ºC). Why wouldn’t it be beneficial to generate power in colder climates for use in warmer areas?
η = 69 %

61. The Second law of Thermodynamics Available Energy
It is impossible to convert a given quantity of heat energy completely into work. In an energy conversion process, energy is always degraded in quality, so that its ability to do work is reduced

62. Summary
1st law – energy is conserved, QH = W + QC (heat in = work and heat out)
Heat engines make use of a flow of heat from hot to cold in order to do work
2nd law limits the amount of work obtainable from a heat engine
Heat energy that flows from the hot source cannot be entirely converted into work; some heat has to be discharged into the environment
Maximum efficiency may be calculated using the Carnot efficiency equation
Total entropy of a system increases in a physical process