Re: [Phys-L] Carnot (?) efficiency of non-Carnot cycles

[Carl Mungan <mungan@usna.edu>]

> The efficiency of any reversible heat engine is the same: 1 - Tcold/Thot.

Hmm… Here we go, all steps to be done reversibly for a monatomic ideal gas.

1. Let initial volume be V at temperature Th. Isothermally expand to 2V: Wout_1 = nRTh*ln2 = Qin_1.

2. Now isochorically depressurize to Th/2 = Tc: Wout_2 = 0, Qin_2 = 1.5nR(Th-Tc) = 1.5nRTh/2.

3. Then isothermally compress back to V: Wout_3 = -nRTh/2*ln2 = Qin_3.

4. Finally isochorically pressure back to Th: Wout_4 = 0, Qin_4 = -1.5nRTh/2.

Define W = Wout_1 + Wout_2 + Wout_3 + Wout_4 = 0.5nRTh*ln2.
Define Qh = Qin_1 + Qin_2 = nRTh(ln2+0.75).
Define Qc = -Qin_3 - Qin_4 = nRTh(0.5ln2+0.75).

check: W = Qh - Qc is true

Define efficiency W/Qh = 0.5ln2/(ln2+0.75) = 0.24015.

No that does not equal 1-Tc/Th = 1-0.5 = 0.5.

I await clarification. -Carl

ps: I only read the digest, so directly cc’ing my email address always appreciated so I don’t have to look up the archives for responses.

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Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/