The volume of a gas is reduced adiabatically to $(1/4)^{th}$ of its initial volume. If the initial temperature is $27\,^{\circ}C$ and $\gamma = 1.4$, the new temperature is:

$A$ polyatomic gas $\left(\gamma = \frac{4}{3}\right)$ is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its volume adiabatically. If its initial pressure is $p$,its new pressure will be (in $p$)

$A$ litre of dry air at $STP$ expands adiabatically to a volume of $3$ litres. If $\gamma=1.40,$ the work done by air is $(3^{1.4}=4.6555)$. [Take air to be an ideal gas] (in $; J$)

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

The variation of pressure $P$ with volume $V$ for an ideal monatomic gas during an adiabatic process is shown in the figure. At point $A$,the magnitude of the rate of change of pressure with respect to volume is

An engine takes in $5$ moles of air at $20\,^{\circ}C$ and $1\,atm$,and compresses it adiabatically to $1/10^{\text{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules,the change in its internal energy during this process is $X\,kJ$. The value of $X$ to the nearest integer is