Liquefaction of Gases and Liquid States

Liquefaction of Gases:

Inversion Temperature (T_i)
\tt T_{i}=\frac{2a}{Rb}
T_i = 2T_b

If the J-Thomson effect is done above the T_i the temperature of gas ↑

In the case of He, H₂ they will get heated when they are subjected to J-T effect.

Critical Temperature (Tc):
The temperature above which a gas can not be liquefied by high pressure is known as Tc.

Critical Pressure(Pc):
The gas having high Tc can be liquefied easily.

Critical Volume (Vc):
The volume occupied by 1 mole of gas at Tc, Pc is called critical volume.
For CO₂; Tc = 30.98°C
Pc = 73.9° atm
Vc = 95.6 ml/mole

Relation between Vander waal's constant (a, b) and Critical constant (Pc, Tc, Vc):
Vc = 3b, Tc = \tt \frac{8a}{27 Rb},\ Pc=\frac{a}{27 b^2}

Compressibility constant (Z) in terms of critical constant:
\tt Z=\frac{P_cV_c}{RT_C}
\tt =\frac{\frac{a}{27 b^2}\left(3b\right)}{R\cdot\left(\frac{8a}{27 Rb}\right)}\Rightarrow Z=\frac{3}{8}=0.375

Relation between Tc, Tb and Ti:
Tc : Tb : Ti = \tt \frac{8}{27}:1:2
\tt P=A\cdot e^{-\frac{\Delta W}{RT}} (P = VP)
H = (Latent heat of vaporisation)
\tt \log P=\frac{-\Delta H}{2.303\ RT}+\log X

y = mx + c
\tt \log \frac{P_2}{P_1}=\frac{\Delta H}{2.303\ R}\left[\frac{1}{T_1}-\frac{1}{T_2}\right]

Surface Tension:
\tt S.T = \frac{W}{a}=J/m² or erg cm^-2
\tt =\frac{F\times l}{l\times l}\Rightarrow S.T=\frac{F}{l}

Viscosity:

\tt F\propto A\times\frac{du}{dz}\Rightarrow F=\eta A\frac{du}{dz}
\tt \eta=\frac{F}{A}\times\frac{dz}{du}
\tt =\frac{N}{m^{2}}\times\frac{m}{ms^{-1}}=N.m^{-2}.s \Rightarrow Pa.S\Rightarrow Kg\ m^{-1}s^{-1}