A monatomic gas at a pressure p having a volume V expands isothermally to a volume 2V 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

1st part : `p_(1)V_(1) = p_(2)V_(2)`
`:. pV = p_(2) xx 2V or, p_(2) = p/2`
2nd part: For adiabatic process
`pV^(gamma)` = constant or, `p_(1) V_(1)^(gamma) = p_(2)^(.) V_(2)^(gamma)`
Here, `p_(1) = p/2, V_(1) = 2V, V_(2) = 16 V, gamma = 5/3`
`:. p_(2)^(.) = p_(1)((V_1)/(V_2))^(gamma) = p/2((2V)/(16V))^(5//3) = p/64`.