An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

$A$ 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:

One mole of an ideal gas expands adiabatically from $200 \,K$ to $250 \,K$. If the specific heat of the gas at constant volume is $0.8 \,kJ \,kg^{-1} \,K^{-1}$, then the work done by the gas is

For an adiabatic expansion of an ideal gas,the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

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

$A$ monoatomic gas is compressed adiabatically to $1/8$ of its initial volume. What happens to the gas pressure? $(\gamma = 5/3)$