The internal energy per mole of an ideal gas is denoted by ${\mathrm{E}}_{\mathrm{ideal}}$. The same for a real gas obeying van der Waals equation is ${\mathrm{E}}_{\mathrm{real}}$. Assuming the average kinetic energy of the molecules of the two gases at the same temperature to be equal, the correct statement for the gas at low pressure is

The isotherms of a gas are shown below :

Among the following,

(i) At ${\mathrm{T}}_1$, the gas cannot be liquefied

(ii) At point $\mathrm{B}$, liquid starts to appear at ${\mathrm{T}}_2$

(ii) ${\mathrm{T}}_{\mathrm{C}}$ is the highest temperature at which the gas can be liquefied

(iv) At point $\mathrm{A}$, a small increase in pressure condenses the whole system to a liquid

The correct statements are :

Among the gases $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}$ and $\mathrm{f}$, the gases that show only positive deviation from ideal behavior at all pressures in the graph are

The volume of gas $\mathrm{A}$ is twice than that of gas $\mathrm{B}$. The compressibility factor of gas $\mathrm{A}$ is thrice than that of gas $\mathrm{B}$ at same temperature. What are the pressures of the gases for equal number of moles?

A gas has a compressibility factor of $0.5$ and a molar volume of $0.4 {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ at a temperature of $800 \mathrm{K}$ and pressure $\mathrm{x} \mathrm{atm}$. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be  $\mathrm{y} {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ . The value of$\mathrm{x}/\mathrm{y}$ is _________

[Use: Gas constant, $\mathrm{R}=8\times {10}^{-2} \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ ]

The variation of the compressibility factor$\left(\mathrm{Z}\right)$with pressure $(\mathrm{P} \mathrm{in} \mathrm{bar})$ for some gases, are shown in the figure below. Identify the gases $\left(\mathrm{A}\right),\left(\mathrm{B}\right)$ and $\left(\mathrm{C}\right)$.