IB Physics HL B.4 Thermodynamics Notes

The first law is an accounting equation. Energy entering the gas by heating either increases the internal energy of the gas or leaves the gas as work done on the surroundings. If a problem uses the opposite sign convention for work, state it clearly and keep it consistent.

State the first law of thermodynamics for a closed gas system and define the sign convention for Q and W.

Gas work is mechanical energy transfer due to a moving boundary such as a piston. The simple equation W = PΔV applies directly for constant pressure. For a changing pressure process, use the area under the p-V curve, with the sign determined by the direction of volume change.

Explain how to determine work done by a gas from a p-V diagram and state the formula for constant pressure.

There are two common routes to internal energy change. In energy-transfer problems, use the first law and the sign convention. In monatomic ideal-gas temperature problems, use the temperature dependence of internal energy. For an ideal gas, a volume change does not by itself determine ΔU unless it also changes temperature.

A monatomic ideal gas changes temperature by ΔT. State how to calculate ΔU and explain how this connects to the first law.

Entropy gives a statistical direction to thermodynamics. A gas spreading out, heat flowing from hot to cold, or energy becoming dispersed are more likely because there are many more microscopic ways to be spread out than concentrated. The word disorder is useful only when tied to this microstate idea.

Explain entropy in terms of microstates and use this to describe why a gas spreading out is spontaneous.

The equation ΔS = Q_rev/T is used for reversible heat transfer or for a thermal reservoir at constant temperature. The statistical equation S = k_B ln(Ω) connects entropy to microstates. Both forms point to the same idea: entropy increases when energy or particles can be arranged in more microscopic ways.

State two equations used to calculate entropy or entropy change, defining all symbols and conditions.

The second law is a direction rule, not a failure of energy conservation. The first law says energy is conserved; the second law says which energy transfers are possible spontaneously. In real processes, total entropy of system plus surroundings increases, or stays constant only for an ideal reversible process.

State two forms of the second law of thermodynamics and explain what they imply about real processes.

Irreversibility is the practical directionality of thermodynamics. Friction converts ordered mechanical energy into dispersed thermal energy, heat flows hot to cold, and gases spread into available volume. These processes are allowed by the first law, but the second law explains why they do not naturally reverse.

A local decrease in entropy is not a loophole in the second law. It means the chosen subsystem is not isolated. A refrigerator lowers entropy inside its cold compartment, but it requires work and releases heat to the room, increasing the entropy of the surroundings by a larger amount.

Each process name tells you what is constrained. Use that constraint to choose the equation, p-V graph shape, and first-law simplification. This is the habit that prevents mixing up a vertical isovolumetric line with a zero-pressure or zero-work process.

Describe the p-V diagram shape and key energy condition for isobaric, isovolumetric, isothermal, and adiabatic processes.

Adiabatic processes are thermally isolated or fast enough that heat transfer is negligible. For a monatomic ideal gas the pressure-volume relation uses γ = 5/3. Combine this with PV = nRT when you need temperature at an initial or final state.

A monatomic ideal gas undergoes an adiabatic expansion. State the pressure-volume relation and explain the temperature change.

Heat engines repeat a set of thermodynamic processes so the working gas returns to its starting state. The useful output is net work per cycle, read from the enclosed p-V area. The second law requires some heat to be rejected; not all heat input can become work in a cyclic engine.

For a heat engine shown as a closed loop on a p-V diagram, explain how to determine net work and ΔU over one cycle.

Efficiency compares what the engine usefully delivers with what it receives. The second law requires some heat rejection in a cyclic engine, so Q_C is not zero for a real engine. Use magnitudes for Q_H and Q_C unless the question defines a signed convention.

A heat engine absorbs Q_H from a hot reservoir and rejects Q_C to a cold reservoir each cycle. State the efficiency equation and explain why η is less than 1 for a real engine.

Carnot efficiency is a limit set by the second law, not a guarantee that an engine reaches that value. Raising the hot-reservoir temperature or lowering the cold-reservoir temperature increases the theoretical maximum, but real engines remain below it because of irreversibility and losses.

Define the Carnot efficiency limit for a heat engine operating between hot and cold reservoirs and state why real engines do not exceed it.

B.4 is an energy-and-entropy toolkit for HL thermodynamics. First account for heat, work, and internal energy; then use p-V diagrams to read processes and cycles; finally use entropy and the second law to explain why real engines and real processes have limits.