An ideal gas at $127^{\circ} C$ is compressed suddenly to $\frac{8}{27}$ of its initial volume. If $\gamma=\frac{5}{3}$ for the ideal gas,then the rise in its temperature is: (in $K$)

The $P-V$ graph of an ideal gas cycle is shown. The adiabatic process is described by the region

Which of the following is the best container for a gas during an adiabatic process?

For an adiabatic process,the pressure and temperature of a monoatomic gas are related as $P \propto T^{c}$. Then,$c = $.......

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:

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.