$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)

$A$ diesel engine has a compression ratio of $20:1$. If the initial pressure is $1 \times 10^5 \ Pa$ and the initial volume of the cylinder is $1 \times 10^{-3} \ m^3$,then how much work does the gas do during the compression (in $J$)? (Assume the process as adiabatic) $(C_V=20.8 \ J/mol \ K, \gamma=1.4, (20)^{1.4}=66.3)$

$A$ triatomic gas at an initial temperature of $18^{\circ}C$ is compressed adiabatically to $1/8$ of its initial volume. What is the final temperature of the gas?

When air of the atmosphere rises up,it cools. Why?

In the provided figure,there is a cyclic process $ABCDA$ on a sample of $1 \, mol$ of a diatomic gas. The temperatures of the gas during the processes $A \rightarrow B$ and $C \rightarrow D$ are $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. Choose the correct option for the work done if processes $BC$ and $DA$ are adiabatic.

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion,respectively. The ratio $T_2 / T_1$ is