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

When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process:

What is an adiabatic process? Derive an expression for work done in an adiabatic process.

$5.6\, L$ of helium gas at $STP$ is adiabatically compressed to $0.7\, L$. Taking the initial temperature to be $T_1$,the magnitude of work done in the process is

One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^{\circ}C$ to $35\,^{\circ}C$. The change in the internal energy of the gas is .... $J$ (given $R = 8.3 \,J/mol/K$)

$A$ 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 $p$)