A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original voume is restored 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. 1.41
C. 1.67
D. 1.83

Answer

B

Explanation

In isothermal process, temperature of the gas remains constant , so the gas obeys Boyle's law .That is,
`pprop(1)/(V)rArr(p_(2))/(p_(1))=(V_(1))/(V_(2))`
`(2p)/(p)=(V_(1))/(V_(2))`
`rArr" " (V_(1))/(V_(2))=2` ....(i)
Now , the gas is expanded adiabaticllay , so
`(p_(1))/(P_(2))=((V_(2))/(V_(1)))^(gamma)rArr(2p)/(0.75p)=((2)/(1))^(gamma)` (since , volume is restroed )
`rArr " " "log" ((8)/(3))=gamma"log"2`
` "log"8-"log"3=gamma"log"2`
`rArr" "gamma=1.41`