Question

An ideal diatomic gas undergoes a process in which its internal energy (U) relates to the volume (V) as U = α , here α is a constant. The internal energy of gas is increased by 100 J.​

Answer 1

$\large\rm{ \gamma = \frac{7}{5} = 1.4}$

Process is $\large\rm{ U = \alpha \sqrt{V}}$

$\large\rm{ \therefore \frac{4}{2} RT = \alpha \sqrt{V}}$

$\large\rm{ \implies T^{2} V^{-1} = K =}$ constant

$\large\rm{ \therefore TV^{- \frac{1}{2}} = K' =}$ constant

on comparing TV^{m-1} = constant we get m-1 = -½

$\large\rm{ \therefore m = \frac{1}{2}}$

$\large\rm{ C = \frac{ R}{ \gamma -1} + \frac{R}{1-m}}$

$\large\rm{ = \frac{R}{1.4-1} + \frac{R}{1.0.5} }$

$\large\rm{ = \frac{9}{2} R}$