$A$ monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one-eighth of its original volume. The final pressure at constant entropy will be $.....P$.

$A$ 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:

$A$ hypothetical gas expands adiabatically such that its volume changes from $8 \ L$ to $27 \ L$. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$, then the ratio of $\frac{C_P}{C_V}$ will be:

When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process:

$A$ sample of $1$ mole of gas at temperature $T$ is adiabatically expanded to double its volume. If the adiabatic constant for the gas is $\gamma = \frac{3}{2}$,then the work done by the gas in the process is:

An ideal gas having initial pressure $P$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $4V$, while its temperature falls to $T/2$. If the work done by the gas during the expansion is $\alpha PV$, the value of $\alpha$ is