n moles of a Vander Waal's gas obeying the equation of state `(P+(n^2a)/V^2)(V-nb)=nRT`, where a and bare gas dependent constants, is made to undergo a cyclic process that is depicted by a rectangle in the PV diagram as shown in the figure. What is the heat absorbed by the gas in one cycle

Options

A. `n(P_1-P_2)(V_2-V_1)`
B. `(P_1-P_2)(V_2-V_1)`
C. `(P_1+(n^2a)/(V_1^2)-P_2-(n^2a)/(V_2^2))(V_1-V_2)`
D. `P_1+(n^2a)/(V_1^2)-P_2-(n^2a)/(V_2^2)(V_2-V_1)`

Answer

B

Explanation

For cycle process : `DeltaU=0`
`thereforeDeltaQ=DeltaU+DeltaW`
`rArrDeltaQ=DeltaW="area under P-V graph"`
`rArrdeltaQ=(P_1-P_2)(V_2-V_1)`