An ideal diatomic gas under goes a process in which its internal energy chnges with volume as given `U=cV^(2//5)` where c is constant. Find the ratio of molar heat capacity to universal gas constant `R` ?

Explanation

From given relation we can write `T prop V^(2//5)`…….(1)
ideal gas equation `implies PV=nRT` ……(2)
form (1),(2) `PV prop V^(2//5)` (or) `PV^(2//5)`=const ………..(3)
Comparing equation (3) with polytropic equation
`PV^(x)=` const, we have `X=(3)/(5)`
`:. C=(R)/(lambda-1)+(R)/(1-x)=5R :. (C)/(R)=5`