Thermal physics

Study H2 Physics temperature, ideal gases and kinetic theory, then internal energy, thermodynamic laws, heat capacity and latent heat.

GCE A-Level H2 Physics 2027
12 lessons

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Before you begin

Temperature, pressure and volume describe a gas from outside; the motion of its molecules explains them from inside. The lessons start with the thermodynamic temperature scale and the ideal gas equation, then use the kinetic theory to derive gas pressure and link temperature to molecular kinetic energy. They go on to internal energy, thermal equilibrium, work done by a gas and the first law of thermodynamics, and finish with specific heat capacity and specific latent heat.

Be comfortable with: impulse and change in momentum, because gas pressure comes from the impulses of molecules hitting the walls.

Learning goals

Use thermodynamic temperature and convert between Celsius and kelvin.
Use ideal-gas equations with particles, moles and SI units.
Apply the kinetic model to gas pressure and mean translational kinetic energy.
Derive pV = ⅓Nm⟨c²⟩ from the definition of pressure and a one-dimensional model of molecular collisions extended to three dimensions.
Relate microscopic energy, internal energy and thermal equilibrium.
Apply work conventions and the zeroth and first laws of thermodynamics.
Define and use heat capacity and specific heat capacity in energy balances.
Define and use specific latent heat in phase-change energy balances.

Syllabus statements covered

show an understanding that a thermodynamic scale of temperature has an absolute zero and is independent of the property of any particular substance
convert temperatures measured in degrees Celsius to kelvin: T/K = T/°C + 273.15
recall and use the equation of state for an ideal gas expressed as pV = NkT, where N is the number of particles
state that one mole of any substance contains 6.02 × 10²³ particles, and use the Avogadro constant Nₐ = 6.02 × 10²³ mol⁻¹ as well as the relationship Nk = nR between the Boltzmann constant and the molar gas constant, where n is the number of moles and N = nNₐ
state the basic assumptions of the kinetic theory of gases
explain how the random motion of gas particles exerts mechanical pressure and hence derive, using the definition of pressure as force per unit area, the relationship pV = ⅓Nm⟨c²⟩ (a simple model considering one-dimensional collisions and then extending to three dimensions using ⟨cₓ²⟩ = ⅓⟨c²⟩ is sufficient)
recall and use the relationship that the mean translational kinetic energy of a particle of an ideal gas is (directly) proportional to the thermodynamic temperature (i.e. ½m⟨c²⟩ = ³⁄₂kT) to solve problems
show an understanding that the macroscopic state of a system determines the internal energy of the system, and that internal energy can be expressed as the sum of a random distribution of microscopic kinetic and potential energies associated with the particles of the system
show an understanding that the thermodynamic temperature of a system is (directly) proportional to the mean microscopic kinetic energy of particles
show an understanding that when two systems are placed in thermal contact, energy is transferred (by heating) from the system at higher temperature to the system at lower temperature, until they reach the same temperature and achieve thermal equilibrium (i.e. no net energy transfer)
show an understanding of the difference between the work done by a gas and the work done on a gas, and calculate the work done by a gas in expanding against a constant external pressure: W = pΔV
recall and apply the zeroth law of thermodynamics that if two systems are both in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other
recall and apply the first law of thermodynamics, ΔU = Q + W, that the increase in internal energy of a system is equal to the sum of the energy transferred to the system by heating and the work done on the system
define and use the concepts of specific heat capacity and specific latent heat

Lessons

Work through them in order.

Core lessons

Practise and check

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Topic reference

Quick reference

Idea	Relation	Notes
thermodynamic temperature	T/K = θ/°C + 273.15	absolute zero is 0 K
equation of state	pV = NkT = nRT	k = 1.38 × 10⁻²³ J K⁻¹, R = 8.31 J mol⁻¹ K⁻¹
moles and particles	N = nNA, Nk = nR	NA = 6.02 × 10²³ mol⁻¹
kinetic theory	pV = (1/3)Nm⟨c²⟩	random motion, elastic collisions
molecular kinetic energy	(1/2)m⟨c²⟩ = (3/2)kT	mean translational kinetic energy
work done by a gas	W = pΔ V	constant external pressure
first law	Δ U = Q + W	Q to the system, W done on it
specific heat capacity	Q = mcΔθ	within one phase
specific latent heat	Q = mL	change of state at constant temperature

Core knowledge to remember

The thermodynamic scale of temperature has an absolute zero and does not depend on the property of any particular substance.
Internal energy is the sum of the random microscopic kinetic and potential energies of the particles of a system; it is determined by the macroscopic state of the system.
Thermodynamic temperature is directly proportional to the mean microscopic kinetic energy of the particles.
Zeroth law: if two systems are both in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.
First law: the increase in internal energy of a system equals the energy transferred to it by heating plus the work done on it.
Specific heat capacity is the energy needed per unit mass per unit rise in temperature; specific latent heat is the energy needed per unit mass to change state at constant temperature.

Common mistakes

Using Celsius temperatures in pV = NkT, (3/2)kT or a temperature ratio.
Using R with a number of molecules, or k with a number of moles.
Squaring the mean speed instead of finding the mean of the squared speeds.
Putting the work done by a gas into Δ U = Q + W as a positive term.
Saying energy flows from the body with more internal energy; it flows from the higher temperature.