Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4 V and then compressed adiabatically to volume V. The final pressure of gas will be (given `gamma=(3)/(2)`)

Options

A. 1P
B. 2P
C. 4P
D. 8P

Answer

B

Explanation

For isothermal process `P_1V_1 = P_2V_2`
`implies PV=P_2 xx 4V implies P_2 = P/4`
For adiabatic process -
`P_2V_2^(gamma)=P_3V_3^(gamma) implies P/4 xx (4V)^(3//2)=P_3(V)^(3//2)`
implies `P_3 =2P`