Unit 5: Thermal Physics

1. Zeroth and First Laws of Thermodynamics

Thermodynamics is the study of heat, work, and temperature. The fundamental laws govern how energy is transferred.

• Zeroth Law: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law defines Temperature.
• First Law: It is a statement of the conservation of energy. It states that the heat added to a system (dQ) is equal to the increase in internal energy (dU) plus the work done by the system (dW).

2. Second Law of Thermodynamics

While the first law asserts energy conservation, the second law dictates the direction of heat flow and the feasibility of energy conversion.

Kelvin-Planck Statement: It is impossible to construct an engine that operates in a cycle and produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work.

Clausius Statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a cooler body to a hotter body.

3. Carnot Engine and Efficiency

The Carnot Engine is a theoretical, ideal reversible heat engine that operates between two temperatures: a source (T1) and a sink (T2).

Processes in a Carnot Cycle:

1. Isothermal Expansion (at T1)
2. Adiabatic Expansion
3. Isothermal Compression (at T2)
4. Adiabatic Compression

4. Concept of Entropy

Entropy (S) is a measure of the molecular disorder or randomness of a system. In a reversible process, the change in entropy is defined as:

Principle of Increase of Entropy: In any natural (irreversible) process, the entropy of the universe always increases. For a reversible process, it remains constant.

5. Kinetic Theory of Gases

This theory explains the macroscopic properties of gases (pressure, temperature) by considering their molecular composition and motion.

Main Postulates:

• Gases consist of large numbers of identical, tiny particles (atoms/molecules).
• Molecules are in constant, random motion and collide elastically.
• The volume of molecules is negligible compared to the total volume of the gas.

6. Maxwell-Boltzmann Distribution of Velocities

In a gas at a certain temperature, not all molecules move at the same speed. The Maxwell-Boltzmann Distribution describes the probability of finding a molecule with a specific velocity.

The peak of the curve represents the Most Probable Speed, which increases and shifts to the right as the temperature rises.

7. Black Body Radiation

A Black Body is an idealized object that absorbs all electromagnetic radiation incident upon it. The radiation it emits depends solely on its temperature.

• Stefan-Boltzmann Law: The total energy radiated per unit surface area is proportional to the fourth power of the absolute temperature (E ∝ T⁴).
• Wien’s Displacement Law: The wavelength of peak emission is inversely proportional to the absolute temperature (λmax ∝ 1/T).