Thermal physics

What thermal physics covers

Heating and temperature first, then the behaviour of gases, then the molecular model that explains why the gas laws take the form they do. The unit contains one of the derivations A-level asks you to reproduce, so the assumptions behind kinetic theory need learning as carefully as the result.

The main ideas

• Solids, liquids and gases described by particle spacing, ordering and motion, and internal energy as the total kinetic and potential energy of the particles in a body.
• Why temperature does not change during a change of state, and calculations with specific heat capacity and latent heat taken stage by stage.
• The electrical determination of a specific heat capacity or latent heat, and how the continuous-flow method cancels the losses.
• The three gas laws with the fixed quantity named each time, and the extrapolation that locates absolute zero.
• The equation of state in both forms, in moles and in molecules, and work done at constant pressure.
• The assumptions of kinetic theory, the derivation that follows, and temperature as a measure of mean molecular kinetic energy.

Key equations

Q = mcΔθ$Q = mc\Delta\theta$Q = mcΔθ

energy for a temperature change, with no change of state

Q = ml$Q = ml$Q = ml

energy for a change of state, at constant temperature

pV = nRT     pV = NkT$pV = nRT \qquad pV = NkT$pV = nRT pV = NkT

the equation of state, in moles and in molecules

W = pΔV$W = p\Delta V$W = pΔV

work done by a gas expanding at constant pressure

pV = 13Nm(c_rms)²$pV = \tfrac{1}{3}Nm(c_{rms})^{2}$pV = (1/3)Nm(c_rms)^2

the result of the kinetic theory derivation

12m(c_rms)² = 3kT2$\tfrac{1}{2}m(c_{rms})^{2} = \frac{3kT}{2}$(1/2)m(c_rms)^2 = 3kT/2

what temperature measures, molecule by molecule

Every equation the thermal physics notes display is collected, with its conditions, on the thermal physics equations page.

Common errors

• Heat and temperature are different quantities. During melting or boiling the energy supplied separates the particles instead of speeding them up, so the temperature holds still while energy continues to flow in.
• Every gas law calculation runs in kelvin. Degrees Celsius give an answer wrong by a factor, and absolute zero is located by extrapolation rather than defined.
• The root mean square speed is not the mean speed. The squares are averaged first and the root taken afterwards, and the order matters.
• The kinetic theory derivation is examinable in full, assumptions included, so it needs practising as a written argument, not just recognising.

Suggested order

Thermal energy transfer first, then ideal gases and the gas laws. Take molecular kinetic theory last, since it explains the empirical laws you have just used, and give the derivation a session of its own.