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The pressure and volume of a monoatomic ideal gas are related as P1V2 for a process A C as shown in the figure. The pressure and volume at A is 3P0 and V0 respectively and the pressure at C is P0. If the molar heat capacity of the ideal gas for the process AC in Rx Find x. (R gas constant) ___

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Solution

The process is described by
P=kv2 Where k is a constant
Let volume at C be V 3P0V20=P0V2V=3V0
W=3V0V0PdV=3V0V0kv2dV=k[1v]3v0v0[1v013v0]=(33)P0V0
Change in internal energy ΔU=f2nRΔT=32nRΔT
ΔT=TcTA=3P0V0nR3P0V0nR=(33)p0v0nR
ΔU=32(33)P0V0
First law of thermodynamics, ΔQ=ΔU+W
ΔQ=22(33)(P0V0+(33)P0V0=12(33)P0V0
AndΔQ=nCΔTnCΔT=12(33)P0V0
n.c(33)P0V0nR=(33)P0V02c=R2

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