$A$ monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $1/8$ of its original volume. What is the final pressure of the gas in terms of $P_1$?

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

An ideal gas is expanded adiabatically at an initial temperature of $300 \ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$.

$A$ diatomic gas undergoes an adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$, where $x$ is:

An ideal gas at $27 \, ^\circ C$ is compressed adiabatically such that its volume becomes $8/27$ of its original volume. If $\gamma = 5/3$ for the gas,the increase in temperature of the gas is ..... $K$.

If the given graph shows the logarithmic values of pressure $(P)$ and volume $(V)$ of an ideal gas, then the ratio of the specific heat capacities of the gas is