Kinetic Theory of Gases:

NCERT References:

• NCERT Class 11 Physics, Chapter 13, “Kinetic Theory of Gases”

• NCERT Class 12 Physics, Chapter 14, “Kinetic Theory and Equations of State”

Detailed Notes:

Assumptions of Kinetic Theory of Gases:

• The gas consists of a large number of tiny, point-like particles called molecules.
• The molecules are in constant, rapid, and random motion.
• The molecules are assumed to be perfectly elastic, meaning there is no loss of kinetic energy during collisions.
• The collisions between molecules are assumed to be instantaneous.
• The molecules are assumed to be non-interacting, meaning there are no forces between them except during collisions.

Microscopic Description of a Gas:

• Molecular mass (M) of a gas is defined as the mass of one mole of the gas.
• Number density (n) of a gas is defined as the number of molecules per unit volume.
• The Boltzmann constant (k) relates the average kinetic energy of a molecule to its absolute temperature.

Molecular Motion and Temperature:

• The average kinetic energy of a molecule is directly proportional to the absolute temperature of the gas.
• The root-mean-square speed of molecules increases with increasing temperature.

Equipartition Theorem:

• The equipartition theorem states that the average kinetic energy of a molecule is equally distributed among all its degrees of freedom.
• For a monatomic gas, there are three translational degrees of freedom, and the average kinetic energy is (3/2)kT.

Specific Heat Capacity:

• The specific heat capacity at constant volume (Cv) is the amount of heat required to raise the temperature of one mole of a gas by 1 K at constant volume.
• The specific heat capacity at constant pressure (Cp) is the amount of heat required to raise the temperature of one mole of a gas by 1 K at constant pressure.
• Cp - Cv = R, where R is the universal gas constant.

Equation of Ideal Gas:

NCERT References:

• NCERT Class 11 Physics, Chapter 13, “Kinetic Theory of Gases”

• NCERT Class 12 Physics, Chapter 14, “Kinetic Theory and Equations of State”

Detailed Notes:

Ideal Gas Law:

• The ideal gas law, also known as the general gas equation, is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.

• The ideal gas law is a mathematical expression of Boyle’s law, Charle’s law, and Avogadro’s law.

Standard Conditions and Molar Mass:

• Standard temperature and pressure (STP) are defined as 0°C (273.15 K) and 1 atm (101.325 kPa), respectively.
• Normal temperature and pressure (NTP) are defined as 25°C (298.15 K) and 1 atm (101.325 kPa), respectively.
• The molar mass of a gas can be determined by measuring its density and using the ideal gas law.

Real Gases and Deviations from Ideal Behavior:

NCERT References:

• NCERT Class 11 Physics, Chapter 13, “Kinetic Theory of Gases”

• NCERT Class 12 Physics, Chapter 14, “Kinetic Theory and Equations of State”

Detailed Notes:

Real Gas Behavior:

• Real gases deviate from ideal behavior due to intermolecular forces and finite molecular volume.

Van der Waal’s Equation:

• Van der Waal’s equation is a modified version of the ideal gas law that takes into account intermolecular forces and finite molecular volume.

(P + a(n/V)^2)(V - nb) = nRT

• The constants a and b are called the Van der Waal’s constants and are characteristic of each gas.

Critical Temperature, Pressure, and Volume:

• The critical temperature (Tc) is the temperature at which a gas can no longer be liquefied by increasing pressure.
• The critical pressure (Pc) is the pressure required to liquefy a gas at the critical temperature.
• The critical volume (Vc) is the volume occupied by one mole of a gas at the critical temperature and pressure.

Andrew’s Isotherms:

• Andrew’s isotherms are a series of curves that show the behavior of real gases at different temperatures and pressures.

Compressibility Factor:

• The compressibility factor (Z) is defined as the ratio of the actual volume of a gas to the volume it would occupy if it behaved ideally at the same temperature and pressure.
• Z = PV/(nRT)
• Z deviates from unity for real gases due to intermolecular forces and finite molecular volume.

By understanding these concepts and practicing related problems, you can strengthen your grasp on Kinetic Theory of Gases and Equation of Ideal Gas, which are essential topics for JEE preparation.