An ideal gas is expanding such that $PT^{3} = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

If $v_1$ is the speed of sound in a diatomic gas at $273^{\circ}C$ and $v_2$ is the r.m.s. speed of its molecules at $273 \ K$,then $\frac{v_1}{v_2}=$

State whether the following statements are True or False:
$(i)$ Due to collision,the density of gas molecules changes.
$(ii)$ The average kinetic energy of $1 \ g$ mass of each gas is equal at the same temperature.
$(iii)$ At the same temperature,the $v_{rms}$ of two different gases is the same.
$(iv)$ At constant temperature,if the pressure of a gas is increased,its mean free path decreases.

The ratio of two specific heats of gas ${C_p}/{C_v}$ for argon is $1.6$ and for hydrogen is $1.4$. Adiabatic elasticity of argon at pressure $P$ is $E$. Adiabatic elasticity of hydrogen will also be equal to $E$ at the pressure

The temperature $(T)$ of one mole of an ideal gas varies with its volume $(V)$ as $T = -\alpha V^3 + \beta V^2$,where $\alpha$ and $\beta$ are positive constants. The maximum pressure of the gas during this process 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?