One mole of gas obey the equation of state P(V - b) = RT and changes its coordinate from `(P_1, V_1)` to `(P_2, V_2)` which is established on P-V diagram by line. The work done in this changes will be _____

Options

A. `1/2(P_2-P_1)(V_2+V_1+2b)`
B. `1/2(P_1+P_2)(V_2-V_1)`
C. `1/2(P_2-P_1)(V_2-V_1)`
D. `1/2(P_1+P_2)(V_2-V_1+2b)`

Answer

B

Explanation

Work done by expansion from `(P_1,V_1)` to `(P_2,V_2)`
W= Area under the graph of `P to V`

`W=1/2` base x height +Area of rectangular
`=1/2(V_2-V_1)xx(P_1-P_2)+(V_2-V_1)P_2`
`=(V_2-V_1)[P_1/2-P_2/2+P_2]`
`=(V_2-V_1)[P_1/2+P_2/2]`
`=1/2(P_1+P_2)(V_2-V_1)`