A diatomic ideal gas is initially at room temperature. It is then heated to a very high temperature such that its vibrational degrees of freedom become fully active. During this process, the ratio of specific heats, = C_P C_V , of the gas:

Step-by-step solution

At room temperature, a diatomic gas has 5 degrees of freedom ( 3 translational and 2 rotational). The ratio of specific heats is given by = 1 + 2 f . For f = 5 , = 1 + 2 5 = 1.4 . At very high temperatures, the vibrational degrees of freedom become active. A diatomic gas gains 2 vibrational degrees of freedom (one for kinetic energy and one for potential energy), making the total degrees of freedom f = 7 . The new ratio of specific heats is = 1 + 2 7 1.28 . Since 1.28 Answer: decreases