The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its initial volume at $27^{\circ}C$. If the value of $\gamma = 1.4$,then the new temperature will be:

The work of $146 \ kJ$ is performed in order to compress one kilo mole of gas adiabatically,and in this process,the temperature of the gas increases by $7 ^\circ C$. The gas is $(R = 8.3 \ J \ mol^{-1} K^{-1})$.

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma = 5/3)$ decreases from $60 \text{ K}$ to $50 \text{ K}$. The work done by the gas in the process is : (Take the universal gas constant as $R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (in $\text{ J}$)

An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

$A$ 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 $4^{1.4} = 6.96]$

$A$ 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