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TPR FL #2 - C/P #57 Work done by gas on environment

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TomBombadil14

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Hello! This is my first time posting on here, so please let me know if I need to add any information or change format!

An ideal gas contained in a piston begins with pressure Po, volume Vo, and temperature To. It undergoes isothermal expansion to volume 2V0. It then undergoes isobaric compression back to volume Vo. Finally its pressure is increased by an isochoric process until it returns to its original state. Which of the following best approximates the work done by the gas on the environment during this sequence?

A) W = 0.
B) 0 < W < P0V0 / 4
C) P0V0 / 4 < W < P0V0 / 2
D) W > P0V0 / 2

I mentally referred back to W=PV. Because the gas returned to its original state PoVo, why isn't the answer A) W=0 ? The answer is B... TPR made a triangle with the 3 states of the gas described and found the area for the work during the process.
 

aldol16

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Work is not a state function. It is path-dependent, much like friction. I would recommend you plot the graph. Work is the area enclosed. It's in the shape of a pseudo-triangle with a concave "hypotenuse." So the area of the pseudo-triangle is smaller than the area of the corresponding triangle. Since the area of the corresponding triangle is 1/2*b*h = 1/2*(Vo)*(1/2P0), the answer is B.
 
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