For an ideal gas ____

Explanation

(i)It is clear that two heat capacities are not equal and `C_P` is greater than `C_V` by a factor who is related to the work done.
(ii) At a constant pressure, a part of heat absorbed by the system is used up in increasing internal energy of the system and the other for doing work by the system.
(iii) At constant volume, the whole of heat absorbed is utilized in increasing the temperature of the system as there is no work done by the system.
Thus `C_P` is greater than `C_V`
`C_P=(dH)/(dT) , C_V=(dU)/(dT)`
(iv ) By definition, H=U+PV for 1 mole of an ideal gas ,
H=U+RT
By differentiating this equation with respect to temperature T, we get ,
`(dH)/(dT)=(dU)/(dT)+R`
`C_P=C_V+R`
`C_P-C_V=R`
Thus for an ideal gas `C_P` is greater than `C_V` by the gas constant R.