The adiabatic elasticity of hydrogen gas $(\gamma = 1.4)$ at $NTP$ is

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure,which of the following is the correct option?

The cross-sectional area of a piston is $8 \times 10^{-3} \, m^2$. The gas has a temperature of $300 \, K$,a pressure of $1.0 \times 10^5 \, Pa$,and a volume of $2.4 \times 10^{-3} \, m^3$. When the gas is heated by a heater,the piston moves by $0.1 \, m$. If the spring constant is $8000 \, N/m$,find the final temperature in $K$.

$\frac{1}{2}$ mole of helium gas is contained in a container at $S.T.P.$ The heat energy needed to double the pressure of the gas,keeping the volume constant (specific heat of the gas $= 3 \; J \; g^{-1} \; K^{-1}$) is ...... $J$.

An ideal gas $(\gamma = 1.5)$ is expanded adiabatically. How many times must the gas be expanded to reduce the root mean square velocity of the molecules $2.0$ times?

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in the same vessel at temperature $T$. The mean square of the velocity of molecules of gas $B$ is $v^2$ and the mean square of $x$ component of the velocity of molecules of gas $A$ is $w^2$. The ratio $\frac{w^2}{v^2}$ is