In which of the following processes,heat is neither absorbed nor released by a system?

During adiabatic expansion,if the temperature of $3$ moles of a diatomic gas decreases by $50^{\circ} C$,then the work done by the gas is (where $R$ is the Universal gas constant). (in $R$)

$A$ polyatomic gas $\left( \gamma = \frac{4}{3} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_0$,its new pressure will be (in $P_0$)

$A$ gas does $4.5 \,J$ of external work during adiabatic expansion. If its temperature falls by $2 \,K$, then its internal energy will be

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:

When a diatomic gas (rigid) undergoes adiabatic change,its pressure $(P)$ and temperature $(T)$ are related as $P \propto T^{c}$. The value of $c$ is