Thermodynamics

Topic-by-topic explanations

1. Introduction

Thermodynamics studies macroscopic systems using state variables such as pressure, volume and temperature and energy transfers as heat and work.

2. Thermal equilibrium

Two systems are in thermal equilibrium if no net heat flows between them when they are placed in thermal contact.

3. Zeroth law of thermodynamics

The zeroth law says if A is in thermal equilibrium with B and B with C, then A is in thermal equilibrium with C. This supports the use of a thermometer.

4. Heat, internal energy and work

Heat is energy transferred due to temperature difference; work is energy transfer by other macroscopic means. Internal energy is the microscopic energy stored in the system.

5. First law of thermodynamics

With the convention ΔQ=ΔU+W, Q is heat added to the system and W is work done by the system. The first law expresses energy conservation; always state the sign convention.

6. Specific heat capacity

Specific heat capacity depends on process. For ideal gases, C_v is molar heat capacity at constant volume and C_p at constant pressure; C_p−C_v=R per mole.

7. Thermodynamic state variables and equation of state

State variables describe the equilibrium state; heat and work are path-dependent transfers. The ideal-gas equation of state is pV=nRT.

8. Thermodynamic processes

Isothermal means constant temperature; for an ideal gas ΔU=0. Adiabatic means Q=0. Isochoric means constant volume and zero boundary work; isobaric means constant pressure.

9. Second law of thermodynamics

The second law gives a preferred direction to natural processes and rules out complete conversion of heat taken from a single reservoir into work in a cycle.

10. Reversible and irreversible processes

Reversible processes are idealised quasi-static changes without dissipative effects. Friction, free expansion and heat transfer across finite temperature differences are irreversible.

11. Carnot engine

A Carnot engine between reservoirs T_h and T_c has maximum efficiency η=1−T_c/T_h; temperatures must be in kelvin. Real engines have lower efficiency.

Formula sheet

Use SI units, state assumptions, show your working and check units before finalising an answer.

Worked example

Common errors and revision checklist

State the first-law sign convention. Use kelvin in Carnot efficiency. Isothermal does not mean zero heat transfer; adiabatic does not imply constant temperature.

• Write the governing law before substituting values.
• Show units and signs/directions.
• Check whether assumptions are satisfied.