Expanding Universe

$\displaystyle \large \frac{hc}{\lambda}$ is the energy of an individual photon.This energy is also proportional to $\displaystyle \large T$ ,the temperature(by kinetic theory)

$\displaystyle \large T \alpha \frac{1}{R}$ R is the radius

$\displaystyle \large t \alpha \frac{1}{V^{\frac{1}{3}}}$

This gives us $\displaystyle \large \gamma$ is $\displaystyle \large \frac{4}{3}$

and then $\displaystyle \large \frac{i+2}{i}$ is $\displaystyle \large \gamma$

$\displaystyle \large i=6$

For this we can assume the photon gas inside a closed ideal box.Where the radiation pressure satisfies $PV=U/3$ .which means $U=3nRT$ .this is equivalent to $Cv=3R$ .But then from equipartition of energy there must be 6 degrees of freedom each with $(kT*1/2)$ energy.