A gas has molar heat capacity `C = 37.55 J "mole"^(-1)K^(-1)`, in the process PT = constant, find the number of degree of freedom of the molecules of the gas.

Answer

`5`

Explanation

`PT` = constant `implies P^(2)V` = constant `implies PV^(1//2)` = constant
For this process `C = C_(V) + (R)/(1-1//2) = C_(V) + 2R`
`implies C_(V) = 37.35 -2 (8.314) = 20.722 = (5)/(2)R`
`implies (f)/(2)R = (5)/(2)R implies f = 5`