An adiabatic process occurs at constant

For an ideal gas,the internal energy is given by $U = 5pV/2 + C$,where $C$ is a constant. The equation of the adiabats in the $pV$-plane will be

Five moles of Hydrogen gas initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas is $(R=8.3 \, J \, mol^{-1} \, K^{-1}, \gamma=1.4$ for diatomic gas$)$ (in $kJ$)

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $E = \frac{U}{V} \propto T^4$ and pressure $P = \frac{1}{3} \left( \frac{U}{V} \right)$. If the shell now undergoes an adiabatic expansion,the relation between $T$ and $R$ is:

An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

$A$ monatomic gas at $630 \,K$ expands adiabatically to $27$ times its initial volume. The final temperature of the gas is (in $\,K$)