In an adiabatic expansion of a gas,the initial and final temperatures are ${T_1}$ and ${T_2}$ respectively. What is the change in internal energy of the gas?

$A$ gas having a volume of $1 \ mm^3$ at $1 \ atm$ pressure is compressed from a temperature of $27^{\circ}C$ to $627^{\circ}C$. What will be the final pressure if the process is adiabatic? (For the gas,$\gamma = 1.5$)

In an adiabatic change,the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P \propto T^C$,where $C$ is equal to:

Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma = 5/3)$ decreases from $60 \text{ K}$ to $50 \text{ K}$. The work done by the gas in the process is : (Take the universal gas constant as $R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (in $\text{ J}$)

$A$ gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is $1.5$, then the percentage decrease in the volume of the gas is