The P-V diagram of path followed by one mole of perfect gas in a cylindrical container is shown in figure, the work done when the gas is taken from state A to state B is

Options

A. `nRTInV_(2)/(V_(1)`
B. `nRTInV_(1)/(V_(2)`
C. `2nRT((V_(1))^(-1/2) - ((V_2)^(-1/2))`
D. `2nRTInV_(1)/(V_(2)`

Answer

B

Explanation

For path A to B
`PV^(3//2)` = constant =A
the work done
`W=overset(V_(2))underset(V_(1))int PdV=overset(V_(2))underset(V_(1))(A)/(V^(3//2))dV=A[(V^(-1//2))/(-1//2)]^(V_(2))`
`=-2A[(V^(-1//2))]_(V_(1))^(V_(2))=-2A[(1)/(sqrt(V_(2))-(1)/(sqrt(V_(1))]`
`=2A[(1)/(sqrt(V_(1))-(1)/(sqrtV_(2))]=2P_(1)V_(1)^(3//2)[(sqrt(V_(2))-sqrt(V_(1))/(sqrt(V_(1)V_(2))]`
`=2P_(1)V_(1)[(1-sqrt(V_(1))/(sqrt(V_(2)])`