For a gas sample with $N_0$ number of molecules, the function $N\left(V\right)$ is given by, $N\left(V\right)=\frac{dN}{dV}=\left(\frac{3N_0}{V_0^3}\right)V^2$ for $0<V<V_0$ and $N\left(V\right)=0$ for $V>V_0$. Where $dN$ is a number of molecules in speed range $V$ to $V+dV$. The rms speed of the molecules is

A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. The order of the most probable speed $v_{\mathrm{p}}$ of the molecules at these five states is,

One mole of an ideal gas undergoes a process in which, $T=T_0+a{V}^3$, where $T_0$ and $a$ are positive constants and $V$ is volume. The minimum pressure attainable is,

The volume thermal expansion coefficient of an ideal gas at constant pressure is

(Here $T=$ absolute temperature of gas)

Consider a hypothetical gas with molecules that can move along only a single axis. The following table gives four situations, the velocities in meter per second of such a gas having four molecules. The plus and minus sign refer to the direction of the velocity along the axis.

In which situation the root-mean-square speed of the molecules is greatest?