Since I was unable to copy a picture of the PV diagram, here is a description of

Question

Since I was unable to copy a picture of the PV diagram, here is a description of it:

Point A to B runs vertical with the pressure increasing from Po to 2Po with no change in volume. The Volume increases from Vo to 2Vo from point A to C and B to C. The pressure decreases back to Po at point C. The cycle is the shape of a triangle.



An ideal gas at pressure, volume, and temperature, P0, V0, and T0, respectively, is heated from point A to point B, allowed to expand to point C (at the same temperature as point B, 2T0), and then returned to the original condition, point A. The internal energy decreases by 3 P0V0/2 going from point C to point A. In going around this cycle once, which quantity equals zero?
A. the net change in internal energy of the gas

B. the net work done by the gas

C. the net heat added to the gas

D. All three of the above are zero.

Explanation / Answer

In going around this cycle once, the net change in internal energy of the gas is equals to zero. For the cyclic process, internal energy U = nCv T here, number of moles of ideal gas = n molar specific heat at constant volume = Cv change in temperature = T In this case, since the initial and final temperatures are equal, then the change in temperature is equal to zero. Therefore, the internal energy U = nCv T                                                    = nCv (0)                                                    = 0 therefore, the correct answer is        option - A) the net change in internal energy of the gas is zero change in temperature = T In this case, since the initial and final temperatures are equal, then the change in temperature is equal to zero. Therefore, the internal energy U = nCv T                                                    = nCv (0)                                                    = 0 therefore, the correct answer is        option - A) the net change in internal energy of the gas is zero

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