A given mass of gas is compressed isothermally untal its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restore and its pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately

Options

A. `1.20`
B. `1.4`
C. `1.67`
D. `1.83`

Answer

B

Explanation

Let P and V be the initial pressure and volume of the gas. Then
For isothermal compression, `P_(1) = P = V_(1) = V, P_(2) = 2P, V_(2) = ?`
As `P_(1)V_(1) = P_(2)V_(2) :. PV = 2PV_(2)` or `V_(2) = (PV)/(2P) = (V)/(2)`
For adiabatic expansion, `P_(1) = 2P, P_(2) = 0.75P, V_(1) = (V)/(2) , V_(2) = V`
As `P_(1)V_(1)^(gamma) = P_(2)V_(2)^(gamma) :. (2P) ((V)/(2))^(gamma) = (0.75P)(V)^(gamma)`
or `0.375 = ((1)/(2))^(gamma)`
Solving, we get `gamma = 1.41`