Question

11. Cu dent for gases. (f) The internal energy of a real gas depends onl 3.83 Show that (@Cyl@V), = 0 for an ideal gas. 3.84 Calculate the work done during the isothermal, reversible expan 1 . 11 .

Answer 1

Solution:

($\partial$Cv/$\partial$V)T = 0 ( for ideal gas)

Proof:

Since,

Cv = ($\partial$ U/$\partial$T)v

Differentiating equation with respect to V at constamT, we get,

($\partial$Cv/$\partial$V)_T = [$\partial$/$\partial$V ( $\partial$ U/$\partial$T)v] _T  = [$\partial$/$\partial$T ( $\partial$ U/$\partial$V)_T]v

The term ( $\partial$ U/$\partial$V)_T = internal pressure and for ideal gases internal pressure = 0

Hence,

($\partial$Cv/$\partial$V)_T = [$\partial$/$\partial$T x 0]v = 0

Hence, proved.