Another contradiction in thermodynamics?

Thread starter Amin2014
Start date Feb 23, 2015
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Carnot cycle Contradiction Friction Second law of thermodynamics Thermodynamics

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The discussion centers on the efficiency of a quasi-static cycle of an ideal gas that experiences friction, contrasting it with the ideal Carnot cycle. It is established that the efficiency of the quasi-static cycle (ηirrev) is lower than that of the reversible Carnot cycle (ηrev) due to energy losses from friction. Participants explore the implications of friction on work calculations, emphasizing the need to consider the combined system of the gas and piston while accounting for external pressures and frictional forces. The conversation highlights the complexity of applying thermodynamic principles in the presence of friction and the need for careful analysis of energy transfers. The discussion remains open-ended as participants plan to further investigate the effects of friction on the system's efficiency.

Feb 26, 2015

Chestermiller

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Amin2014 said:

The work done by the gas is ∫PdV. We have (P- P_c)V^gamma = Const, so we substitute P in terms of V to evaluate the integral. By "total work". I assume you mean ∫P_extdV, which can readily be found from -PdV + (F/A)dV = -P_extdV. For part d, I think we can define two different efficiencies, one with the work done by the gas in the numerator and one with the total work as numerator.

I have another method for you to consider (not involving further integration).

We have nC_vdT=-P_extdV, so the total work done on the surroundings is -nC_vΔT.
The integral of (F/A)dV is the work to overcome friction, (F/A)ΔV. So the work done by the gas is -nC_vΔT+(F/A)ΔV
For the efficiency, I get the total work done on the surroundings divided by the work done by the gas.

Chet