The amount of work done in an adiabatic expansion from temperature $T$ to ${T_1}$ is

$A$ gas is compressed adiabatically until its temperature is doubled. The ratio of its final volume to initial volume will be

The heat capacity of one mole of an ideal gas is found to be $C_V = \frac{3R(1 + aRT)}{2}$,where $a$ is a constant. The equation obeyed by this gas during a reversible adiabatic expansion is

$A$ monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to $(\frac{1}{8})^{\text{th}}$ of its initial volume. The ratio of final pressure to initial pressure is (in $:1$)

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?

In an adiabatic change,the pressure $P$ and temperature $T$ of a monoatomic gas are related by the relation $P \propto T^C$,where $C$ equals