Kinetic Theory Of Gases And Equation Of Ideal Gas Topic
Formulae and Equations related to Kinetic Theory of Gases and Ideal Gas Laws: 1. Mean free path of a gas molecule:
Where:
- (\lambda) is the mean free path in meters (m)
- (k_B) is the Boltzmann constant ( 1.380649 \times 10^{-23} \ J/K)
- (T) is the temperature in Kelvin (K)
- (d) is the molecular diameter in meters (m)
- (P) is the pressure in Pascals (Pa)
2. Graham’s law of effusion:
Where:
- (r_1) and (r_2) are the effusion rates of two different gases.
- (M_1) and (M_2) are the molar masses of the two gases.
3. Adiabatic expansion of an ideal gas:
Where:
- (P) is the pressure.
- (V) is the volume.
- (\gamma) is the ratio of specific heats (C_P/C_V)
4. Van der Waals equation of state for real gases:
Where:
- (a) and (b) are constants that depend on the gas
- (n) is the number of moles of gas.
- (R) is the ideal gas constant.
5. Compressibility factor:
Where (Z) is compressibility factor.
6. Heat capacity at constant volume of an ideal gas:
Where:
- (C_{V}) is the heat capacity at constant volume in joules per Kelvin per mole ( J/(mol-K)).
- (n) is the number of moles of gas
- (R) is the ideal gas constant.
7. Heat capacity at constant pressure of an ideal gas:
Where:
- (C_P) is the heat capacity at constant pressure in joules per Kelvin per mole ( J/(mol-K)).
- (n) is the number of moles of gas
- (R) is the ideal gas constant.
