T-V curve of cyclic process is shown below, number of moles of the gas are n find the total work done during the cycle.

Options

A. `(3)/(2) nRT_(0) In 2`
B. `nRT_(0) In 2`
C. `(nRT_(0) In 2)/(2)`
D. `2 nRT_(0) In 2`

Answer

B

Explanation

Since path `AB` and `CD` are isochoric therefore work done is zero during path `AB` and `CD`. Process `BC` and `DA` are isothermal therefore,
`W_(BC) = nR2T_(0)1n(V_C)/(V_B) = 2nRT_(0)1n2`
`W_(DA) = nRT_(0)1n(V_A)/(V_D) = -nRT_(0)1n2`
Total work done
`W_(BC)+W_(DA)=2nRT_(0)1n 2=nRT_(0) 1n 2`.