P-V curve of a diatomic gas is shown in the Fig. Find the total heat given to the gas in the process `A rarr B rarr C`

Options

A. `P_(0) V_(0) + 2P_(0) V_(0) "in" 2`
B. `(1)/(2)P_(0) V_(0) + P_(0) V_(0) "in" 2`
C. `(5)/(2)P_(0) V_(0) + 2P_(0) V_(0) "in" 2`
D. `3P_(0) V_(0) + 2P_(0) V_(0) "in" 2`

Answer

C

Explanation

From first law of thermodynamics
`DeltaQ_(ABC) = DeltaU_(ABC)+DeltaW_(ABC)`
`DeltaW_(ABC)=DeltaW_(AB)=0+nRT_(B)In2(V_C)/(V_B)`
`=nRT_(B)In(2V_0)/(V_0)`
`=nRT_(B)In2 = 2P_(0)V_(0)In2`
`DeltaU = nC_VDeltaT = 5/2(2P_(0)T_(0))`
`implies DeltaQ_(ABC) = 5/2P_(0)V_(0)+2P_(0)V_(0)In2`.