A cycle followed an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure The heat exchanged by the engine with the surroundings at constant volume is (Take `C_(V)=(3)/(2)R)`

Options

A. `(P_(B)-P_(A))V_(A)`
B. `(1)/(2)(P_(B)-P_(A))V_(A)`
C. `(3)/(2)(P_(B)-P_(A))V_(A)`
D. `(5)/(2)(P_(B)-P_(A))V_(A)`

Answer

C

Explanation

In the given figure portion AB of the cycle shows increase in pressure/ temperature of gas at constant volume Therefore system gains heat from the surroundings ,then

`Q_(AB)=U_(AB)=nC_(V)DeltaT`
`Q_(AB)=1xxC_(V)xxDeltaTxxDeltaT=(3)/(2)R(T_(B)-T_(A))=(3)/(2)(P_(B)V_(B)-P_(A)V_(A))`
`Q_(AB) = (3)/(2)(P_(B)-P_(A))V_(A)`