$A$ monoatomic ideal gas is compressed adiabatically to $12.5 \%$ of its initial volume. If the initial temperature of the gas is $T_1 \ K$ and the final temperature is $xT_1 \ K$,the value of $x$ is:

$A$ tyre filled with air ($27^\circ C$ and $2 \text{ atm}$) bursts. What is the final temperature of the air in $^\circ C$? (Given: $\gamma = 1.5$)

$A$ cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) compartments at the same $P, V, T$. Heating is started from the left side until the pressure changes to $\frac{27P}{8}$. If the initial volume of each compartment was $9 \text{ litres}$, then the final volume in the right-hand side compartment is . . . . . . litres. (for this ideal gas $\gamma = C_P/C_V = 1.5$)

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} C$ is $W$. Then, the work done on heating $6$ moles of rigid diatomic gas through the same change in temperature is: (in $W$)

$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given,$\gamma = 3/2$):

The work done in an adiabatic change in an ideal gas depends upon only