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. `2.5 P_(0) V_(0)`
B. `1.4 P_(0) V_(0)`
C. `3.9 P_(0) V_(0)`
D. `1.1 P_(0) V_(0)`

Answer

C

Explanation

c. `Q_(AB) = Delta U_(AB) + W_(AB)`
`W_(AB) = 0`
`Delta U_(AB) = (f)/(2) nR Delta T`
`(f)/(2) (Delta PV) Delta U_(AB) = (5)/(2) (Delta PV)`
`Q_(AB) = 2.5 P_(0) V_(0)`
Process `BC, Q_(BC) = Delta U_(BC) + W_(BC)`
`= 0 + 2 P_(0) V_(0) log 2 = 1.4 P_(0) V_(0)`
`Q_(n e t) = Q_(AB) + Q_(BC) = 3.9 P_(0) V_(0)`