Lecture 11

Lecture 11 - Chem 338 Lecture 11 Heat Engines 1. Boltzmann:...

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Chem 338 C h em 3 3 8 L e c t u r e 1 1 Heat Engines 1. Boltzmann: S = k B ln W Provides the link from molecular to macroscopic 2. Entropy: dS = dq rev /T Macroscopic analysis of devices 3. The Carnot Cycle: a. Heat Engines: η < (T H –T C ) / T H b. Air Conditioners: < T C /(T H –T C ) c. Heat Pumps: < T H /(T H –T C ) 4. Partition Functions: S = U/T + k B ln Q
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Chem 338 0 ! ! j B N j B j j Bj j j j j j j jj j j j j j j j j j j Sk W g kN N N Ng NN N dS k g dN N dN dN N g dS k d N Nd N N dN dN N = ⎧⎫ ⎪⎪ = ⎨⎬ ⎩⎭ =− + + ⎡⎤ ⎢⎥ ⎣⎦ ⎛⎞ ⎜⎟ ⎝⎠ == ±²²³²²´ ln ln ln ln ln ln ln ln 1. Boltzmann: S = k B ln W Provides the link from molecular to macroscopic W W k k
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Chem 338 () 1 1 j Bj j j B jj j B j rev g dS k dN N dS k q N dN dN kT dN T dq dS T ⎡⎤ ⎛⎞ = ⎢⎥ ⎜⎟ ⎝⎠ ⎣⎦ ⎧⎫ =− + ⎨⎬ ⎩⎭ = = ∑∑ E ln ln ln j B j B j j jB Ng Nq g q N N g qN Nk T e e = = + ln ln ln
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Chem 338 2. Entropy: dS = dq rev /T Macroscopic devices
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Chem 338 3. The Carnot Cycle: 0 First Law dU = v 0 0 univ Second Law dS S = Δ≥ v
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Lecture 11 - Chem 338 Lecture 11 Heat Engines 1. Boltzmann:...

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