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

For isothermal process `P_(1)V_(1) = P_(2)V_(2)`
`rArr PV = P_(2)(2V) rArr P_(2) =P/2`
For adiabatic process
`P_(2)V_(2)^(Y) = P_(3)V_(3)^(Y)`
`rArr (P/2) (2v)^(gamma) = P_(3)16^(gamma) rArr P_(3) = 3/2 (1/8)^(5//3) = P/64`