One mole of an ideal gas is initially at pressure P1. volume V1, and temperature

Question

One mole of an ideal gas is initially at pressure P1. volume V1, and temperature T1, represented by point A on the PV diagram above. The gas is taken around cycle ABCA shown. Process AB is isobaric, process BC is isochoric. and process CA is isothermal. Calculate the temperature T2 at the end of process AB in terms of temperature T1. Calculate the pressure A at the end of process BC in terms of pressure P1. Calculate the net work done on the gas when it is taken from A to B to C. Express your answer in terms of P1 and V1. Indicate below all of the processes that result in heat being added to the gas. Justify your answer.

Explanation / Answer

From A to B, pressure is constant and volume decreases by ahalf, so temperature does also. So... .       T2 = (1/2)T1 . Temperature at C is the same as temperature at A, so theproduct PV must be the same. Since volume was halved, pressure isdoubled, so pressure at C is... .          p2 = 2p1 . Work done A to B =   p V =   p1 (1/2) V1  =    (1/2) p1 V1 . Work done B to C is zero so .      total work done A to B to C = (1/2) p1V1 . Heat is added to gasin BC and CA, but not in AB (heat isreleased from gas there) . Heat is added to gasin BC and CA, but not in AB (heat isreleased from gas there)

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