During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_P}{C_V}$ for the gas is

The $P-V$ diagram of a diatomic ideal gas system undergoing a cyclic process is shown in the figure. The work done during the adiabatic process $CD$ is (use $\gamma=1.4$) (in $J$):

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

$A$ motor-car tyre has a pressure of $2\,atm$ at $27\,^{\circ}C$. It suddenly bursts. If $\gamma = (C_p/C_v) = 1.4$ for air,find the resulting temperature.

$A$ gas having $\gamma = 5/2$ and volume $360 \text{ c.c.}$ is suddenly compressed to $90 \text{ c.c.}$ If the initial pressure of the gas is $P$,then the final pressure will be:

$A$ reversible adiabatic path on a $P-V$ diagram for an ideal gas passes through state $A$ where $P = 0.7 \times 10^5 \, N/m^2$ and $V = 0.0049 \, m^3$. The ratio of specific heats of the gas is $1.4$. The slope of the path at $A$ is: