A monatomic, ideal gas is in a sealed container (the number of gas molecules is

Question

A monatomic, ideal gas is in a sealed container (the number of gas molecules is always constant);
the initial pressure is P1 = 1.14 x 105 Pa and the initial volume is V2 = 0.0571 m3.

First, the volume of the gas is decreased at a constant pressure (at P1 = 1.14 x 105 Pa) to a volume of V1 = 0.0501 m3.

Second, the pressure of the gas is increased at a constant volume (at V1 = 0.0501 m3) to a pressure of P2 = 1.48 x 105 Pa.

Third, the volume of the gas is increased at a constant pressure (at P2 = 1.48 x 105 Pa) back to the original volume of V2 = 0.0571 m3.

Fourth, the pressure of the gas is decreased at a constant volume (at V2 = 0.0571 m3) to its original pressure of P1 = 1.14 x 105 Pa.

How much heat was added to (give as a positive number) or removed from (give as a negative number) the system? Q = ?
(The gas constant R = 8.31 J/mole-K.)

Explanation / Answer

Since in a cyclic process, work done = 0

Thus, heat added/removed in the process = area enclosed by the process in the PV-diagram

Hence heat = (P2 - P1)*(V2 - V1) = {(1.48 - 1.14)*105}*(0.0571 - 0.0501) = 238 J

Thus, heat is added to the system = 238 J

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