If a gas of volume $400 \ cc$ at an initial pressure $P$ is suddenly compressed to $100 \ cc$,then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is $1.5$).

One gram mole of a diatomic gas $(\gamma = 1.4)$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $127^{\circ}C$. The work done will be:

The bulk modulus of a gas is defined as $B = -V (dp / dV)$. For an adiabatic process,the variation of $B$ is proportional to $p^n$. For an ideal gas,$n$ is:

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$, then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$.

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5 \ L$ to $4 \ L$. The ratio of initial pressure to final pressure is:

$A$ gas $(\gamma = 1.5)$ is suddenly compressed to $(1/4)^{th}$ of its initial volume. Find the ratio of its final pressure to its initial pressure.