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LearnAQA7408First teaching 2015Paper 2 · Paper 2Thermal physics

Paper 2 · Module

Thermal physics

5 subtopics≈ 170 min in total

Start the module: Internal energy Open graphing calculator

Internal energy
The internal energy of a system is the sum of the random kinetic and potential energies of its molecules. It depends only on the state of the system (its temperature, volume, phase), not on how it got there. A rise in temperature means more random kinetic energy. During a change of state the potential energy changes while the temperature stays constant. For an ideal gas there are no intermolecular forces, so internal energy is all kinetic: $U=\tfrac32NkT$ .
≈ 30 min
Thermal equilibrium and temperature scales
Thermal energy flows from hotter to colder regions until they reach the same temperature: thermal equilibrium. Any property that changes with temperature (length of mercury, resistance, thermocouple e.m.f.) can make a thermometer, but different properties don't agree between fixed points. The thermodynamic scale doesn't depend on any substance: its zero is absolute zero, and $T/\text{K}=\theta/°\text{C}+273.15$ .
≈ 30 min
The ideal gas equation
One mole contains $N_A=6.02\times10^{23}$ particles. An ideal gas obeys $pV=nRT$ , where $n$ is the number of moles, $R=8.31$ J mol⁻¹ K⁻¹ and $T$ is in kelvin. Equivalently $pV=NkT$ , with $N$ molecules and the Boltzmann constant $k=\dfrac R{N_A}=1.38\times10^{-23}$ J K⁻¹. Boyle's law, Charles's law and the pressure law are special cases.
≈ 35 min
Kinetic theory of gases
Gas pressure comes from molecules colliding with the walls, each collision changing momentum. Under the kinetic theory assumptions, $pV=\tfrac13Nm\langle c^2\rangle$ . Comparing with $pV=NkT$ gives the mean translational kinetic energy of a molecule: $\tfrac12m\langle c^2\rangle=\tfrac32kT$ . Temperature is a direct measure of average molecular kinetic energy; the r.m.s. speed is $\sqrt{\langle c^2\rangle}$ .
≈ 40 min
Specific heat capacity and latent heat
Specific heat capacity $c$ is the energy needed per unit mass per unit temperature rise: $Q=mc\Delta\theta$ . Water's $c$ is about $4200$ J kg⁻¹ K⁻¹. Specific latent heat $L$ is the energy needed per unit mass to change state at constant temperature: $Q=mL$ . Vaporisation needs much more energy than melting because molecules must be completely separated and push back the atmosphere.
≈ 35 min