Thermal Physics
What the exam tests
This domain covers thermal equilibrium, ideal gases, kinetic theory, internal energy and the first law of thermodynamics. Questions often require the ideal gas equation, kinetic theory relationships and energy accounting during a thermodynamic process.
Core rules
- The zeroth law defines thermal equilibrium: if A is in equilibrium with B and B with C, then A is in equilibrium with C.
- Ideal gas equation: pV = nRT, with T in kelvin. Boltzmann form: pV = NkT.
- Mean kinetic energy of a gas molecule = (3/2)kT; root-mean-square speed vrms = √(3RT/M).
- Internal energy of an ideal gas depends only on temperature.
- First law: Q = ΔU + W, where W is work done by the gas. For constant pressure, W = pΔV = nRΔT.
- During a change of state, temperature remains constant while latent heat is supplied.
Worked example
0.50 mol of an ideal gas is heated at constant pressure and its temperature rises by 40 K. If 400 J of heat is supplied, find the work done by the gas and the change in internal energy. Take R = 8.31 J mol⁻¹ K⁻¹. W = pΔV = nRΔT = 0.50 × 8.31 × 40 = 166 J. Using Q = ΔU + W: ΔU = 400 − 166 = 234 J. The gas does 166 J of work and its internal energy increases by 234 J. The remaining energy is stored as increased molecular kinetic energy.
Traps
Using degrees Celsius in pV = nRT; reversing the sign of work done on the gas; using molar mass instead of gas constant; assuming all supplied heat raises temperature during melting or boiling; forgetting that ideal internal energy does not depend on pressure or volume.