LAWS OF PERFECT GASES

LAWS OF PERFECT GASES

• PERFECT/ IDEAL GAS:-

Those gases obey all the gas law under all condition of pressure and temperature.

• GAS LAW:-

1. Boyel's Law: -

 V∝ 1/P     (When temperature is constant)

2. Charle's Law: -

V ∝ T     (When pressure is constant) [T = Absolute Temperature]

3. Gay-Lussac Law: -

P ∝T   (When volume is constant) [T = Absolute Temperature]

4. Joule’s Law: -

The internal energy of an ideal gas does not change if volume and pressure change, but does change if temperature changes.

5. Avogadro's Law: -

Equal volume of all gases and vapors under the same condition of pressure and temperature contain identical no of molecules.

V ∝ n

Avogadro’s number: - 6.023x 10²³

At NTP, 1 mole of all gases occupies a volume of 22.4 litters.

6. Regnault's Law: -

Sp. Heat of gas remains constant at all temperature and pressure.

7. Dalton's Law: -

The pressure exerted by a mixture of gases is equal to the sum of the pressure exerted by the individual gases having the mixture volume and mixture temperature, provided the gases are not miscible.

• GENERAL GAS EQUATION: -

V ∝ 1/P                 (When temperature is constant)

V ∝ T                    (When pressure is constant)

PV ∝ T                  (When pressure and temperature both are variable)

PV = CT [C =Constant]

Pv = RT    [For 1 kg gas] v_s= Specific Volume

mPv= mRT  [For 'm' kg of gas] R= Characteristic Gas constant

Therefore, PV = mRT

P = (m/V)RT

P = ρRT

SI unit of R is J/kgK or N-m/kg-K.

Value of R is different for different gases. (For Atmospheric Air, R =287J/kgK)

 

For ‘n’ mole gas-

PV = nR_uT [n = no of mole] n =(W/M) Where W = weight of gas and M= Moleculer weight of gas.

R_u= Universal Gas constant.

Unit of Ru is J/mol K

Value of Ru is 8.314kJ/kg-mol K or 848kgf-m/mol K.

 

• SPECIFIC HEAT OF GAS:

Specific Heat at constant volume:

Amount of heat required to be added or rejected to/by a unit mass of gas for 1⁰ increase or decrease temperature at constant Volume.

Q = m.c_v.dT

If, m = 1kg and dT = 1⁰, Then c_v= Q

OR, Rate of change of specific internal energy with respect to temperature at constant volume process.

c_v= (du/dT)_v

Molar specific heat at constant volume: - C_vm= M. c_v

 

Specific Heat at constant pressure:

Amount of heat required to be added or rejected to/by a unit mass of gas for 1⁰ increase or decrease temperature at constant pressure.

Q = m.c_p.dT

If, m = 1kg and dT = 1⁰ ,Then c_p = Q

OR, Rate of change of enthalpy with respect to temperature at constant pressure process.

C_p = (dh/dT)p

Molar specific heat at constant pressure: - C_pm= M. c_p

THERMODYNAMIC PROCESS OF PERFECT GAS