During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_v}$ for the gas is

The average degree of freedom per molecule of a gas is $6$ . The gas performs $25\ J$ work, while expanding at constant pressure. The heat absorbed by the gas is   …. $J$

The $P-V$ diagram of $2\,g$ of helium gas for a certain process $A \to B$ is shown in the figure. What is the heat given to the gas during the process $A \to B$

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

One mole of an ideal gas $(C_p/C_v = \gamma )$ at absolute temperature $T_1$ is adiabatically compresses from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by