During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of (C_(P))/(C_(V)) for the gas is

During an adiabatic process, the pressure of a gas is found to be prop

1.	During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of (C_(P))/(C_(V)) for the gas is
Answer» `(5)/(3)` `(3)/(2)` `(4)/(3)` 2 Solution :`P prop T^(3)` `PT^(-3)` = constant …(i) For an adiabatic process, `PT^(gamma//1-gamma)` = constant …(ii) Comparing (i) and (ii), we get `(gamma)/(1-gamma) = -3` or `gamma = -3 + 3gamma` or `-2gamma = -3` or `gamma = (3)/(2)` As `gamma = (C_(P))/(C_(V)) :. (C_(P))/(C_(V)) = (3)/(2)`