Question

The internal energy E of a system is given by E=bS^3/VN , where b is a constant and other
symbols have their usual meaning. The temperature of this system is equal to

Answer 1

solution-

given data

energy of system(E)=$\frac{bS^3}{VN}$

by applying the first law of thermodynamics

$TdS=dE+pdV$

and

$dE=TdS-pdV$

at the constant volume change in internal energy with respect to entropy is known as temperature

so,

$(\frac{\partial E}{\partial S})_v=T$ .......eq1

by putting the value of E in equation 1

$(\frac{\partial\frac{bS^3}{VN} }{\partial S})_v=T$

and by partial derivative

temperature can be shown as below

$T=3\frac{bS^2}{VN}$