During an adiabatic compression,$830 \ J$ of work is done on $2 \ moles$ of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperature is nearly..... $K$ $(R = 8.3 \ J \ K^{-1} \ mol^{-1})$

$A$ 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 expansion respectively,then $T_1/T_2$ is given by

The relation obeyed by a perfect gas during an adiabatic process is $PV^{3/2} = \text{constant}$. The initial temperature of the gas is $T$. When the gas is compressed to half of its initial volume, the final temperature of the gas is:

In an adiabatic change,the pressure $P$ and temperature $T$ of a monoatomic gas are related by the relation $P \propto T^C$,where $C$ equals

Helium at $27^oC$ has a volume of $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be ....... $^oC$ $[\gamma = 5/3]$

An ideal gas at $27^{\circ}\text{C}$ is compressed adiabatically to $(8/27)$ of its original volume. If $\gamma = 5/3$, then the rise in temperature of a gas is (in $\text{ K}$)