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

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

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

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.

Heat Engine Animations Otto Cycle (automobile) http://www.animatedengines.com/otto.html https://sites.google.com/site/physicsflash/home/otto

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?

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

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!

“Everything” problem – getting efficiency ΔU 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 2000J Net heat absorbed/expelled during cycle 2000 J Change in internal energy during cycle 0 J Efficiency (common sense) 𝑒= 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑢𝑡 𝑓𝑢𝑒𝑙 𝑏𝑖𝑙𝑙 𝑖𝑛 = 𝑛𝑒𝑡 𝑤𝑜𝑟𝑘 ℎ𝑒𝑎𝑡 𝑖𝑛 = 2000 𝐽 11500 𝐽 =17.3%

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

Carnot cycle animation Note cycle bounded by upper and lower isotherms (red/blue) and left and right adiabats (green) http://educypedia.karadimov.info/library/carnot.swf

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!

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

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.

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

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)

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

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 13.41 =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 7.97 =351 𝐽