Gaseous State : Liquification of the gas

 

Degrees of freedom of a gaseous molecule

(1)     The motion of atoms and molecules is generally described in terms of the degree of freedom which they possess.

(2)     The degrees of freedom of a molecule are defined as the independent number of parameters required to describe the state of the molecule completely.

(3)     When a gaseous molecule is heated, the energy supplied to it may bring about three kinds of motion in it, these are,

(i)      The translational motion              

(ii)     The rotational motion                  

(iii)    The vibrational motion. This is expressed by saying that the molecule possesses translational, rotational and vibrational degrees of freedom.

(4)     For a molecule made up of N atoms, total degrees of freedom = 3N. Further split up of these is as follows :

            Translational                       Rotational         Vibrational

            For linear molecule              :         3                 2                 3N – 5

            For non-linear molecule     :         3                 3                 3N – 6

 

Specific and Molar heat capacity of Gases

(1)     Specific heat (or specific heat capacity) of a substance is the quantity of heat (in calories, joules, kcal, or kilo joules) required to raise the temperature of 1g of that substance through . It can be measured at constant pressure (Cp) and at constant volume (CV).

(2)     Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1oC.

∴ Molar heat capacity = Specific heat capacity × Molecular weight,

i.e.,

            CV = cv × M and CP = cp × M

(3)     Since gases upon heating show considerable tendency towards expansion if heated under constant pressure conditions, an additional energy has to be supplied for raising its temperature by 1oC relative to that required under constant volume conditions, i.e.,

            Cp > Cv or Cp = Cv + work done on expansion, PΔV(=R)

Where, Cp = molar heat capacity at constant pressure; CV = molar heat capacity at constant volume.

Note :     Cp and Cv for solids and liquids are practically equal. However, they differ considerable in case of gas because appreciable change in volume takes place with temperature.

 

(4)     Some useful relations of Cp and Cv

(i)      Cp – Cv = R = 2 calories = 8.314 J

(ii)     Cv =  \frac { 3 }{ 2 }  R (for monoatomic gas) and Cv =  \frac { 3 }{ 2 } + x  (for di and polyatomic gas), where x varies from gas to gas.

(iii)    \frac { { C }_{ p } }{ { C }_{ v } } = λ  (Ratio of molar capacities)

(iv)    For monoatomic gas Cv = 3 calories whereas, Cp = Cv + R = 5 calories

(v)     For monoatomic gas, (λ) =  \frac { { C }_{ p } }{ { C }_{ v } } =\frac { \frac { 5 }{ 2 } R }{ \frac { 3 }{ 2 } R } = 1.66.

(vi)    For diatomic gas (λ) =  \frac { { C }_{ p } }{ { C }_{ v } } =\frac { \frac { 7 }{ 2 } R }{ \frac { 5 }{ 2 } R } = 1.40.

(vii)   For triatomic gas (λ) =  \frac { { C }_{ p } }{ { C }_{ v } } =\frac { 8R }{ 6R } = 1.33.  

 

Values of Molar heat capacities of some gases,

Gas Cp Cv Cp– Cv Cp/Cv= g Atomicity
He 5 3.01 1.99 1.661 1
N2 6.95 4.96 1.99 1.4 2
O2 6.82 4.83 1.99 1.4 2
CO2 8.75 6.71 2.04 1.30 3
H2S 8.62 6.53 2.09 1.32 3

 

Liquefaction of gases

(1)     A gas may be liquefied by cooling or by the application of high pressure or by the combined effect of both. The first successful attempt for liquefying gases was made by Faraday (1823).

(2)     Gases for which the intermolecular forces of attraction are small such as H2, N2, Ar and O2, have low values of Tc and cannot be liquefied by the application of pressure are known as “permanent gases” while the gases for which the intermolecular forces of attraction are large, such as polar molecules NH3, SO2 and H2O have high values of Tc and can be liquefied easily.

(3)     Methods of liquefaction of gases : The modern methods of cooling the gas to or below their Tc and hence of liquefaction of gases are done by Linde’s method and Claude’s method.

(i)      Linde’s method : This process is based upon Joule-Thomson effect which states that “When a gas is allowed to expend adiabatically from a region of high pressure to a region of extremely low pressure, it is accompained by cooling.”

(ii)     Claude’s method : This process is based upon the principle that when a gas expands adiabatically against an external pressure (as a piston in an engine), it does some external work. Since work is done by the molecules at the cost of their kinetic energy, the temperature of the gas falls causing cooling.

(iii)    By adiabatic demagnetisation.

 

(4)     Uses of liquefied gases : Liquefied and gases compressed under a high pressure are of great importance in industries.

(i)      Liquid ammonia and liquid sulphur dioxide are used as refrigerants.

(ii)     Liquid carbon dioxide finds use in soda fountains.

(iii)    Liquid chlorine is used for bleaching and disinfectant purposes.

(iv)    Liquid air is an important source of oxygen in rockets and jet-propelled planes and bombs.

(v)     Compressed oxygen is used for welding purposes.

(vi)    Compressed helium is used in airships.

 

(5)     Joule-Thomson effect : When a real gas is allowed to expand adiabatically through a porous plug or a fine hole into a region of low pressure, it is accompanied by cooling (except for hydrogen and helium which get warmed up).

Cooling takes place because some work is done to overcome the intermolecular forces of attraction. As a result, the internal energy decreases and so does the temperature.

Ideal gases do not show any cooling or heating because there are no intermolecular forces of attraction i.e., they do not show Joule-Thomson effect.

During Joule-Thomson effect, enthalpy of the system remains constant.

Joule-Thomson coefficient. μ = (∂T/∂P)H. For cooling, μ = +ve (because dT and dP will be –ve) for heating μ = –ve (because dT = +ve, dP = –ve). For no heating or cooling μ = 0 (because dT = 0).

(6)     Inversion temperature : It is the temperature at which gas shows neither cooling effect nor heating effect i.e., Joule-Thomson coefficient μ =0. Below this temperature, it shows cooling effect and above this temperature, it shows heating effect.

Any gas like H2, He etc, whose inversion temperature is low would show heating effect at room temperature. However, if these gases are just cooled below inversion temperature and then subjected to Joule-Thomson effect, they will also undergo cooling.