The state of an ideal gas is changed through an isothermal process at temperature `T_0` as shown in figure. The work done by the gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is `(p_0)/(2)`, then the pressure of the gas in state C is

Options

A. `p_0/3`
B. `p_0/4`
C. `p_0/6`
D. `p_0/8`

Answer

D

Explanation

`W=nRT_01n((p_i)/(p_f))`
`W_(BC)=2W_(AB)`
`:.` `nRT_0 In((p_C)/(p_0//2))=2nRT_0 In((p_0//2)/(p_0))`
Solving this equation we get,
`p_C=p_0/8`