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 restoreand its pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately

A given mass of gas is compressed isothermally untal its pressure is d

1.	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 restoreand its pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately
Answer» `1.20` `1.4` `1.67` `1.83` Solution :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`