Thermodynamics & Kinetic Theory of Gases (KTG) Quick Revision

Thermodynamics

• Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.  
• First Law of Thermodynamics: The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
  • ΔU = Q - W
   
• Second Law of Thermodynamics: It is impossible to construct a heat engine that operates with 100% efficiency.
  • Kelvin-Planck Statement: No heat engine can convert all the heat absorbed from a reservoir into work.
  • Clausius Statement: Heat cannot be transferred from a colder body to a hotter body without work being done.
   
• Third Law of Thermodynamics: It is impossible to reach absolute zero temperature.
• Thermodynamic Processes:
  • Isothermal: Temperature remains constant.
  • Adiabatic: No heat exchange with surroundings.
  • Isobaric: Pressure remains constant.
  • Isochoric: Volume remains constant.
• Carnot Cycle: A theoretical cycle that represents the maximum possible efficiency for a heat engine.
  • Efficiency = 1 - (T₁/T₂)

Kinetic Theory of Gases

• Ideal Gas Law: PV = nRT
  • P: Pressure
  • V: Volume
  • n: Number of moles
  • R: Gas constant
  • T: Temperature
• Kinetic Energy of a Gas Molecule: KE = (3/2)kT
  • k: Boltzmann constant
• Root Mean Square (RMS) Speed of Gas Molecules: v_rms = √(3RT/M)
  • M: Molar mass
• Mean Free Path: Average distance traveled by a gas molecule between collisions.
  • λ = (1/√2) * (πd²/n)
  • d: Diameter of gas molecule
• Maxwell-Boltzmann Distribution: Describes the distribution of molecular speeds in a gas.
• Specific Heat Capacity: Amount of heat required to raise the temperature of a unit mass of a substance by 1 degree Celsius.
  • Cv: Specific heat capacity at constant volume
  • Cp: Specific heat capacity at constant pressure
  • Cp - Cv = R

Important Formulas:

• Work done by a gas: W = ∫PdV
• Heat added to a gas: Q = ΔU + W
• Internal energy of a gas: U = (3/2)nRT

Remember:

• Practice solving numerical problems.
• Understand the concepts and their applications.
• Review key formulas and their derivations.