A monatomic gas at a pressure P, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V. The final pressure of the gas is ( take `gamma=5/3`)

Options

A. 64 P
B. 32 P
C. P/64
D. 16 P

Answer

C

Explanation

If `P_2` is pressure after isothermal expansion, then
`P_2V_2=P_1V_1 , P_2=P_1V_1/V_2=PxxV/(2V)=P/2 `
If P3 is pressure after adiabatic expansion, then
`P_2V_2^(gamma)=P_3V_3^(gamma)`
`P_3=P_2 (V_2/V_3)^gamma=P/2((2V)/16)^(5//3) = P/2 (1/8)^(5//3)`
`=P/2(1/2^3)^(5//3) =P/2xx1/2^5 =P/64`