A certain gas has a ratio of specific heats equal to at a given temperature. When the temperature is increased, the gas molecules acquire additional modes of motion such that the number of degrees of freedom becomes twice its initial value. The new ratio of specific heats for the gas is:

Step-by-step solution

The ratio of specific heats is related to the number of degrees of freedom f by the equation: = 1 + 2 f From this, the initial degrees of freedom can be written as: f = 2 - 1 When the number of degrees of freedom doubles, the new degrees of freedom f' is: f' = 2f = 4 - 1 The new ratio of specific heats ' is then: ' = 1 + 2 f' = 1 + 2 ( 4 - 1 ) ' = 1 + - 1 2 = + 1 2 Answer: + 1 2