## States of Matter: Gases and Liquids

# Liquefaction of Gases and Liquid States

**Liquefaction of Gases:**

Gas | Liquid | Liquefaction takes place | |

Attraction | Less | More | on increasing 'P' |

KE | More | Less | on decreasing 'T' |

**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, H_{2} 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 CO_{2}; 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/m^{2} 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}

### Part1: View the Topic in this Video from 0:11 to 10:45

### Part2: View the Topic in this Video from 37:55 to 53:40

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