# lec19 - 1 ± dS | Q H | ≤ T H 1 ± 2 ± ± 2 ± ± 1 ±...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Heat Engine Takes a substance around a closed cycle Heat is put into the substance and taken out Work is taken out Eﬃciency, η (work out) / (heat in) 8.044 L19B1
Closed cycle U = ∆ Q +∆ W = 0 Q = W Q /Q P HEAT IN d 1 (HOT RESERVOIR) HEAT OUT 2 1 = d /Q /Q + d 1 2 2 ≡| Q H | ≡−| Q C | (COLD RESERVOIR) V 8.044 L19B2

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Most General Case W out = W = ∆ Q = | Q H | − | Q C | W out η = | Q H | − | Q C | = 1 | Q C | | Q H | | Q H | | Q H | Very Special Case Example: Carnot Cycle Any substance Isothermal and adiabatic changes 8.044 L19B3
P T 1 1' 2 2' Q=0 1' 2 2' 1 T H T C Q=0 S V /Q < T dS Use the second law: d 8.044 L19B4a

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P T 2' 2 1 1' S 1' 2 2' 1 T H T C Q=0 Q=0 V DRAWN TO SCALE FOR AN IDEAL GAS: PV=NkT T H = 1.5 T C S HIGH - S

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Unformatted text preview: 1 ± dS | Q H | ≤ T H 1 ± 2 ± ± 2 ± ± 1 ± dS, use dS = − 1 dS −| Q C | ≤ T C 2 2 ± 1 ± T C ≤ − T C 1 dS ⇒ | Q C | ≥ T C ± 1 1 ± dS and | Q C | | Q H | ≥ T H T C η = 1 − | Q C | | Q H | ≤ 1 − T H 8.044 L19B5 Arbitrary Engine Cycle d /Q ≤ T dS for each element along the path. ± 2 ± 2 ± 2 d /Q 1 T dS ≤ T max dS 1 1 ² ³´ µ ≤ ² ³´ µ positive | Q H | 8.044 L19B6 ± 2 ² 1 ² 1 d /Q ≤ 2 T dS, both sides are negative ² 1 ² 1 T dS | ≥ T min | Q C | ≥ | 2 | 2 dS | ² 2 T min | 1 dS | since dS = 0 ≥ T min | Q C | | Q H | ≥ T max T min η = 1 − | Q C | ≤ 1 − T max | Q H | 8.044 L19B7 Carnot cycle in a pure thermodynamic approach Q C T C Used to deﬁne temp. η = 1 − | Q H | • | | ≡ 1 − T H • Used to deﬁne the entropy /Q d ± d ≤ 0 /Q is an exact diﬀerential T ⇒ T 8.044 L19B8...
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