$A$ gas at $37^{\circ} C$ is compressed adiabatically to half of its volume. What is the final temperature of the gas (in $^{\circ} C$)? (Ratio of specific heat capacities of the gas is $1.5$)

In an adiabatic expansion of an ideal gas,the product of pressure and volume:

In an adiabatic process,if the pressure is increased by $\frac{2}{3}\% $ and the ratio of specific heats $\frac{C_p}{C_v} = \gamma = \frac{3}{2}$,then the volume decreases by about:

$A$ monoatomic ideal gas is compressed adiabatically to $12.5 \%$ of its initial volume. If the initial temperature of the gas is $T_1 \ K$ and the final temperature is $xT_1 \ K$,the value of $x$ is:

$A$ certain mass of gas at $273 \ K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^\circ C$

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: