For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to liquefaction. Choose the correct statement.

at T = 500 K, P = 40 atm, the state will be liquid.

at T = 300 K, P = 50 atm, the state will be gas.

at T < 300 K, P > 20 atm, the state will be gas.

at 300 K < T < 500 K, P > 50 atm, the state will be liquid.

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Which is the correct relation between Boyle temperature and critical temperature of a real gas?

$\mathrm{T}_{\mathrm{B}}=\mathrm{T}_{\mathrm{C}}$

$\mathrm{T}_{\mathrm{B}}>\mathrm{T}_{\mathrm{C}}$

$\mathrm{T}_{\mathrm{B}}<\mathrm{T}_{\mathrm{C}}$

$\mathrm{T}_{\mathrm{B}} \leq \mathrm{T}_{\mathrm{C}}$

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Liquefaction of Gases

Liquefaction of Gases
Liquefaction of gases is done under the following two conditions: (i) Low temperature (i) High pressure

Low Temperature: As the temperature of the gas is lowered, the kinetic energy of the molecules decreases. The volume occupied by the gas also decreases. At very low temperature molecules come Very close to each other, later, on coming more closer they ultimately change into the liquid state.
High Pressure: Increase in pressure brings the gaseous molecules closer and closer to one another. So, this factor also helps in converting the gas into liquid.

For each gas there is a certain temperature above which the gas cannot be liquefied however high pressure is applied. Therefore we can say that the effect of temperature is more important than that of the pressure.

Critical Temperature T_c
Critical temperature of a gas may be defined as that temperature above which the gas cannot be liquefied however high the pressure is applied on the gas.

Critical Pressure P_c
The minimum pressure that must be applied on a gas at its critical temperature to just liquefy it.

Critical Volume V_c
The volume occupied by one mole of a gas at its critical temperature and critical pressure is known as the critical volume.

Significance of a and b

It gives the magnitude of attraction forces present between gas molecules.
Liquefication of gases ∝ a
Hence more the value of 'a' or force of attraction between the molecules of a gas more will be its liquefaction:
Example,
$\begin{array}{l}{\text { Values of 'a' }} \\ {\text { He }<\mathrm{H}_{2}<\mathrm{O}_{2}<\mathrm{N}_{2}<\mathrm{CO}_{2}<\mathrm{HCl}<\mathrm{NH}_{3}<\mathrm{SO}_{2}} \\ {\mathrm{a} \rightarrow(0.034)(0.244)(1.36)(1.39)(3.59)(3.8)(4.17)(6.71)} \\ {\text { Increasing order of liquefication of some gases }}\end{array}$
Its constancy in value shows that gas molecules are incompressible.
$\mathrm{b=4 N\left(\frac{4}{3} \pi r^{2}\right)}$
At low pressure 'a' dominates but at high pressure 'b' dominates.