Three moles of an ideal gas `(C_p=7/2R)` at pressure, `P_A` and temperature `T_A` is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure `P_A`.
(a) Sketch P-V and P-T diagrams for the complete process.
(b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete process.

Explanation

`n=3`,`P_1=P`,`V_1=V`,`T_1=T`
`1rarr2`:`PV=P_2.2VimpliesP_2=(P)/(2)`,`T_2=T`
`2rarr3`:`P_3=P_2=(P)/(2)`,`(2V)/(T)=(V)/(T_3)impliesT_3=(T)/(2)`
(a)
(b) `1rarr2` (Isothermal expansion),
`DeltaW_(1rarr2)=nRT1n((2V)/(V))=3RT1n2`
`2rarr3` (Isobaric compression)
`DeltaW_(2rarr3)=nRDeltaT=3R((T)/(2)-T)=-1.5RT`
`3rarr1` (Isochoric process)
`DeltaW_(3rarr1)=0`
`Delta_(cyclic)=DeltaW_(1rarr2)+DeltaW_(2rarr3)+DeltaW_(3rarr1)`
`=RT(3ln2-1.5)`
`=RT(3xx0.693-1.5)=0.58RT`
For cyclic process
`DeltaQ=DeltaW`
`=0.58RT`