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.

Explanation

Here, `C=37.55 J "mole"^(-1) K^(-1) , and PT=K("constant")` ..(i)
According to standard gas equation `PV = RT` or `P = RT//V`
From (i), `(RT)/V xx T = K or V = (RT^(2))/(K) :. (dV)/(dT) = (2RT)/(K)`
But `T/K = 1/p` from (i) therefore, `(dV)/(dT) = (2R)/(P)` ...(ii)
As, `C =C_(upsilon) + P(dV)/(dt)`, therefore, using (ii)
`C = C_(upsilon) + P xx (2R)/(P) = C_(upsilon) + 2R or C_(upsilon)=C -2R`
as `C_(upsilon) = n/2 R :. n/2 R =C- 2R or n=(2(C-2R))/(R) = (2(37.55 - 2xx 8.3))/(8.3) =5`.