One mole of an ideal gas at an initial temperature of $T \, K$ does $6 \, R \, \text{joules}$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$, the final temperature of the gas will be

$A$ diatomic gas of volume $2 \ m^3$ at pressure $2 \times 10^5 \ N \ m^{-2}$ is compressed adiabatically to a volume $0.5 \ m^3$. The work done in this process is,$[$Use $4^{1.4} = 6.96]$

$1 \, \text{kmol}$ of an ideal gas is compressed adiabatically,requiring $146 \, \text{kJ}$ of work. During this process,the temperature of the gas increases by $7^o \text{C}$. The gas is: $(R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1})$

$A$ 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. If $l_{1}$ and $l_{2}$ are the lengths of the gas column before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

$A$ monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $1/8$ of its original volume. What is the final pressure of the gas in terms of $P_1$?

In an adiabatic expansion,the product of pressure and volume: