Thermodynamics
A-Level Physics 9702 · Topic 16 revision notes · A2
Internal energy, work done by and on a gas, and the first law of thermodynamics as energy conservation for heating and work.
4 definitions to learn word for word, 5 equations in their own column, 6 diagrams and graphs. Read it, cover it, test yourself.
- 16.1 Internal energy
- 16.2a Work done by and on a gas
- 16.2b The first law of thermodynamics
Definitions (mark-scheme wording)EquationsExam traps
16.1Internal energy
Definitions
- Internal energy
- the sum of a random distribution of kinetic and potential energies of the molecules in a system.
Key points
- Internal energy is determined by the state of the system, not by how it reached that state.
- A rise in temperature raises the mean random kinetic energy of the molecules, so internal energy increases.
- During a change of state at constant temperature, the potential energy part of U changes, not the kinetic part.
- Ideal gas: no intermolecular forces, so potential energy = 0 and U is kinetic energy only.
- So for an ideal gas U ∝ T: ΔU = 0 whenever the temperature is unchanged.
- Monatomic ideal gas: U = N × (3/2)kT = (3/2)nRT.
Internal energy: random kinetic energy (motion) plus potential energy (intermolecular forces).
Ideal gas: U depends on T alone (straight line through the origin in kelvin).
Watch out!
- For an ideal gas U depends on temperature alone: an isothermal change has ΔU = 0.
- Internal energy is random energy; the kinetic energy of the whole container moving does not count.
16.2aWork done by and on a gas
Definitions
- Work done by a gas
- the work done when a gas expands against an external pressure; at constant pressure it equals pΔV.
- Work done on a gas
- the work done by the surroundings when the gas is compressed.
Key points
- Gas at pressure p pushes a piston of area A with force F = pA; moving Δx gives W = pAΔx = pΔV.
- Expansion: the gas does work on the surroundings. Compression: work is done on the gas.
- W = pΔV holds only at constant pressure.
- In general, work done = area under the p-V graph.
- No volume change (rigid container) means no work is done.
A gas at pressure p pushes the piston out by Δx: work done by the gas = pΔV.
Work done = area under the p-V graph (a rectangle pΔV at constant pressure).
Watch out!
- Convert volumes to m3 before using W = pΔV (1 cm3 = 10-6 m3).
- Do not use W = pΔV when the pressure changes; use the area under the p-V graph.
16.2bThe first law of thermodynamics
Definitions
- First law of thermodynamics
- the increase in internal energy of a system is equal to the sum of the thermal energy supplied to the system and the work done on the system.
Key points
- Signs: q = thermal energy supplied to the gas; W = work done on the gas.
- Compression: W positive. Expansion: W negative (the gas does work).
- Heat lost by the gas: q negative. Temperature rises: ΔU positive.
- Isothermal (constant T, ideal gas): ΔU = 0, so q = -W.
- Constant volume: W = 0, so ΔU = q.
- No heat exchange (rapid or insulated): q = 0, so ΔU = W; a gas compressed this way warms, one expanding cools.
- Complete cycle: back to the same state, so ΔU = 0; net work = area enclosed by the loop.
First law in a cylinder: heating q and work W done on the gas both raise its internal energy.
A cycle ABCDA: ΔU = 0 over the cycle; the enclosed area is the net work done by the gas (clockwise loop).
Watch out!
- Get the sign of W right: an expanding gas has W negative in ΔU = q + W.
- Isothermal does not mean q = 0; it means ΔU = 0. It is the insulated (no heat flow) change that has q = 0.