1. Heat Engines Heat Engines. First Law and Heat Engines Carnot cycle.
Refrigerators & Air conditioners.
Heat Pumps.
2nd Law considerations.
Entropy.

2. Heat engines Examples of Heat Engines Each of these has Steam engine
Coal plant
Nuclear plant
Automobile
Jet engine
Each of these has
Hot source
Cold source
Path from hot to cold which can be diverted to work
Expanding piston steam engine, car engine
Pressure difference across turbine blade

3. Steam engine Path from hot to cold which can be diverted to work
Expanding piston steam engine.
Pressure difference across turbine blade.

4. Internal combustion engine
Path from hot to cold which can be diverted to work
Expanding piston car engine.
Hot reservoir inside engine, cold reservoir tailpipe
“Internal combustion” engine.

5. Heat Engine Animations
Otto Cycle (automobile)

6. First Law and Heat Engines
Expand gas at high temperature and pressure to create work.
Compress gas at low temperature and pressure to restore original.
Work out expanding greater than work in compressing.
Requires operating between high temperature/pressure and low temperature/pressure.
Requires extracting heat from hot source and expelling to cold source, diverting difference to work.
Efficiency typically low 𝐸= 𝑊 𝑁𝑒𝑡 𝑄 𝐻
What is most efficient cycle?

7. Heat Engine efficiency
Extract heat from hot source, expel some to cold source, divert some to work.
Leave out details of P/V/T variation.
Efficiency definition (economic)
𝑒= 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑦𝑜𝑢 𝑔𝑒𝑡 𝑜𝑢𝑡 𝐹𝑢𝑒𝑙 𝑏𝑖𝑙𝑙 𝑦𝑜𝑢 𝑝𝑢𝑡 𝑖𝑛
𝑒= 𝑊𝑜𝑟𝑘 𝑄 𝐻
𝑒= 𝑄 𝐻 − 𝑄 𝐿 𝑄 𝐻 =1− 𝑄 𝐿 𝑄 𝐻

8. Efficiency Example Efficiency Definition 𝑒= 𝑊𝑜𝑟𝑘 𝑄 𝐻
𝑒= 𝑊𝑜𝑟𝑘 𝑄 𝐻
0.2= 23,000 𝐽 𝑄 𝐻
𝑄 𝐻 =115 𝑘𝐽
Balancing Energies
𝑄 𝐻 − 𝑄 𝐿 =𝑊𝑜𝑟𝑘
115 𝑘𝐽 − 𝑄 𝐿 =23 𝑘𝐽
𝑄 𝐿 =92 𝑘𝐽
Must waste 92 kJ!

9. “Everything” problem – getting efficiencyΔU
Work Q
a -> b
+6000 J
+4000 J
10000 J
b -> c
-4500 J
0 J
c -> d
-3000 J
-2000 J
-5000 J
d -> a
+1500 J
1500 J
entire cycle
2000 J
Net work during entire cycle J
Net heat absorbed/expelled during cycle J
Change in internal energy during cycle J
Efficiency (common sense)
𝑒= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑢𝑡 𝑓𝑢𝑒𝑙 𝑏𝑖𝑙𝑙 𝑖𝑛
= 𝑛𝑒𝑡 𝑤𝑜𝑟𝑘 ℎ𝑒𝑎𝑡 𝑖𝑛 = 2000 𝐽 𝐽 =17.3%

10. Carnot cycle – most efficient cycle
Isothermal, adiabatic boundaries.
Add/remove heat isothermally
Raise/lower temperature adiabatically
Heat ratio equals temperature ratio
𝑄 𝐿 𝑄 𝐻 = 𝑇 𝐿 𝑇 𝐻
Efficiency Definition
𝑒=1− 𝑄 𝐿 𝑄 𝐻
For Carnot Cycle
=1− 𝑇 𝐿 𝑇 𝐻

11. Carnot cycle animation
Note cycle bounded by upper and lower isotherms (red/blue) and left and right adiabats (green)

12. Carnot cycle examples 𝑒 𝑐𝑎𝑟𝑛𝑜𝑡 =1− 𝑇 𝐿 𝑇 𝐻 =1− 543 𝐾 773 𝐾 =0.3
𝑒 𝑐𝑎𝑟𝑛𝑜𝑡 =1− 𝑇 𝐿 𝑇 𝐻 =1− 543 𝐾 773 𝐾 =0.3
𝑒 𝑐𝑎𝑟𝑛𝑜𝑡 =1− 𝑇 𝐿 𝑇 𝐻 =1− 285 𝐾 435 𝐾 =0.34
𝑒 𝑐𝑙𝑎𝑖𝑚𝑒𝑑 = 𝑊𝑜𝑟𝑘 𝑄 𝐻 = 𝑄 𝐻 − 𝑄 𝐿 𝑄 𝐻 =0.56
Can’t Work!

13. Forward and reverse Carnot cycle
Forward Carnot cycle (heat engine)
QH in
Work, QL out
Clockwise cycle
Reverse Carnot cycle (refrigeration)
Work, QL in
QH out
Counterclockwise cycle

14. Refrigeration – Heat Engine in Reverse
Basic Operation
Compress gas and liquefy to high temperature/pressure
Cool liquefied gas at high pressure (Q out)
Expand gas and evaporate to low temperature/pressure
Warm evaporated gas at low pressure (Q in)
Thermodynamic cycle running backwards.

15. Forward and reverse Carnot animation
Forward animation (heat engine)
educypedia.karadimov.info/library/AF_2202.swf
Reverse animation (refrigeration)
educypedia.karadimov.info/library/AF_2205.swf

16. Efficiency, Coefficient of Performance
Heat Engine
𝑒= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑊 𝑄 𝐻
= 𝑄 𝐻 −𝑄 𝐿 𝑄 𝐻
= 𝑇 𝐻 −𝑇 𝐿 𝑇 𝐻 (Carnot)
Refrigerator
𝐶𝑂𝑃= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑄 𝐿 𝑊
= 𝑄 𝐿 𝑄 𝐻 − 𝑄 𝐿
= 𝑇 𝐿 𝑇 𝐻 − 𝑇 𝐿 (Carnot)
Heat pump
𝐶𝑂𝑃= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑄 𝐻 𝑊
= 𝑄 𝐻 𝑄 𝐻 − 𝑄 𝐿
= 𝑇 𝐻 𝑇 𝐻 − 𝑇 𝐿 (Carnot)

17. Example 15-13 QH delivered to inside (winter):
𝐶𝑂𝑃= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑄 𝐻 𝑊 𝑄 𝐻 =3.0∙1500 𝑊=4500 𝑊
QL taken from outside (winter):
𝑄 𝐿 = 𝑄 𝐻 −𝑊=4500 𝑊 −1500 𝑊=3000 𝑊
QL taken from inside (reversed - summer)
𝐶𝑂𝑃= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑄 𝐿 𝑊 = 3000 𝑊 1500 𝑊 =2.0

18. Heat Pump - Problem 32 at 0° C at -15° C
𝐶𝑂𝑃 𝑐𝑎𝑟𝑛𝑜𝑡 = 𝑇 𝐻 𝑇 𝐻 − 𝑇 𝐿 = 295 𝐾 295 𝐾−273 𝐾 =13.41
𝐶𝑂𝑃= 𝑄 𝐻 𝑊 𝑊= 𝑄 𝐻 𝐶𝑂𝑃 = 2800 𝐽 =209 𝐽
at -15° C
𝐶𝑂𝑃 𝑐𝑎𝑟𝑛𝑜𝑡 = 𝑇 𝐻 𝑇 𝐻 − 𝑇 𝐿 = 295 𝐾 295 𝐾−258 𝐾 =7.97
𝐶𝑂𝑃= 𝑄 𝐻 𝑊 𝑊= 𝑄 𝐻 𝐶𝑂𝑃 = 2800 𝐽 =351 𝐽