Lesson summary
16. Thermodynamics — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Define internal energy, calculate the work done by or on a gas, and apply the first law of thermodynamics with the correct sign convention.Internal energy U = th…
- State dependence
- Definition wording
- Solids and liquids
- Real gases
- Proportionality
- Kelvin only
Section 1 of 7What internal energy is
- Internal energy U = the sum of the random distribution of kinetic and potential energies of the molecules in a system.
- Kinetic energy comes from the random motion (speed) of the molecules.
- Potential energy comes from the intermolecular forces and changes with their separation.
- State dependence
- for a fixed mass at its melting or boiling point, the liquid has more internal energy than the solid and the gas more than the liquid.
- Definition wording
- the energies and motion must be described as random.
Section 2 of 7Changing internal energy
| Internal energy increases when… | Internal energy decreases when… |
|---|---|
| Thermal energy is added (the system is heated) | Thermal energy is lost to the surroundings |
| Work is done on the system, for example by compressing a gas | The system does work on its surroundings, for example a gas pushing a piston |
Section 3 of 7Internal energy and temperature
- Solids and liquids
- molecules are close with intermolecular forces, so they have kinetic and potential energy, and vibrate more when heated.
- Real gases
- molecules also have potential energy from intermolecular forces, and heating makes them move faster.
- Ideal gas
- there are no intermolecular forces, so potential energy is zero and the internal energy is the total kinetic energy of the molecules, (3/2)NkT.
- Proportionality
- the internal energy is directly proportional to the temperature in kelvin, U ∝ T, and ΔU ∝ ΔT.
- Kelvin only
- tripling the Celsius temperature does not triple U.
Section 4 of 7Work done by an expanding gas
- Constant pressure
- a gas pushes back its surroundings and does work on them, W = pΔV.
- p is the external pressure of the surroundings, not the pressure of the gas.
- ΔV is the final volume minus the initial volume, in m3.
- Piston
- a gas in a cylinder pushes the piston out a distance s with force F = pA, so work = Fs = pAs = pΔV.
- Examples
- steam pushing a piston in an engine and a balloon inflating against atmospheric pressure.
Section 5 of 7Work done on a gas
- Compression
- a force must push the piston in, which needs work and reduces the volume.
- Effect on the gas
- the molecules speed up, so their kinetic energy and the temperature increase.
- Sign convention
- in the first law, W is the work done on the system.
| Process | Work term W | Reason |
|---|---|---|
| Gas expands | Negative (−) | The gas does work on the surroundings |
| Gas is compressed | Positive (+) | The surroundings do work on the gas |
Section 6 of 7The first law of thermodynamics
- First law of thermodynamics = the increase in internal energy of a system equals the thermal energy added to it plus the work done on it.
- It is energy conservation, and applies to every thermodynamic system, not only gases.
- Equation
- ΔU = q + W.
| Symbol | Positive means | Negative means |
|---|---|---|
| ΔU | Internal energy rises | Internal energy falls |
| q | Thermal energy added to the system | Thermal energy removed from the system |
| W | Work done on the system | Work done by the system |
Section 7 of 7Using the first law
- Decide the direction of each energy transfer and give it the correct sign.
- Find the work from W −pΔV for an expansion (positive for a compression), using the external pressure.
- Find q from the information given, for example a latent heat when a substance changes state.
- Substitute into ΔU q + W and check the sign is physically sensible.
- Boiling a liquid
- heat is added (q positive) and the vapour expands against the atmosphere (W negative),
- but internal energy rises because q is greater than the work done.
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