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`

Explanation

From first law of thermodynamics
`Delta Q _(ABC) =Delta u _(ABC) + Delta W_(ABC)`
`Delta W _( ABC) = Delta W _(AB) + Delta W _(BC)`
`0+ nRT _(B) ln (V _(C))/(V _(B)) =nRT _(B) ln (2 V_(0))/(V_(0))`

`= nRT _(B) ln 2 = 2 P _(0) V _(0) ln 2`
`Delta u =n C _(v) Delta T =5/2 (2P _(0) V _(0) -P_(0)V_(0))`
`implies Delta Q _(ABC) =5/2 P _(0) V_(0) + 2P_(0) V_(0) ln 2.`