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Thermodynamics

The first law, the four processes and the heat engine. Read work, heat and internal energy off a P–V graph with the sign convention fixed.

Questions in the bank
125
q/paper in 2025–26
1.07
Numeric answer
17%
Notes pages
6

Tier: Core

When you’ll see it

A gas taking in heat or doing work: a named process, a path on a P–V graph, a cycle, an adiabatic change, or an engine between two temperatures.

How this chapter is tested

Thermodynamics is a core chapter, set about once a paper. One law carries it: the heat given to a gas goes into its internal energy and into the work it does, Q = ΔU + W, with work done by the gas counted positive. The process decides how that heat splits, and adiabatic processes alone take a large share of the questions.

Many questions come with a P–V graph. Work is the area under the path, and its sign comes from the direction: a leg towards smaller volume is negative work, and a clockwise cycle does positive net work. Read each axis on its own scale before using πab for an elliptical cycle.

ΔU = nCvΔT in every process, so the usual slips are Cp used for ΔU, γ − 1 replaced by γ, and a Celsius temperature put into an efficiency. The degrees of freedom behind Cv come from Kinetic Theory, and the Carnot page closes the chapter with T₂/T₁ in kelvin.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • First law

    ΔQ = ΔU + W with work by the gas positive; for a liquid that boils, ΔU is the latent heat minus PΔV.

  • Internal energy and heat capacities

    ΔU = nCvΔT in every process; Cv = fR/2 and Cp = Cv + R; for PVˣ = constant, C = Cv + R/(1 − x), which can be negative.

  • Processes and P–V work

    Each standard process zeroes one term of the first law; work is the signed area under the path; for PVˣ = constant, W = nR(T₁ − T₂)/(x − 1), with nRT ln(V₂/V₁) when x = 1.

  • Adiabatic processes

    PV^γ, TV^(γ−1) and P^(1−γ)T^γ stay constant; W = −ΔU = nR(T₁ − T₂)/(γ − 1); the adiabat is steeper than the isotherm by the factor γ.

  • Cyclic processes

    ΔU = 0 round a cycle, so net heat equals net work, the enclosed area, positive when clockwise; work each leg after finding its corner pressures.

  • Engines and refrigerators

    η = W/Q₁ and, for Carnot, 1 − T₂/T₁ in kelvin; a refrigerator's COP = Q₂/W = T₂/(T₁ − T₂); engines in series give η₁ + η₂ − η₁η₂.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Cp used for ΔU

    The heat at constant pressure is nCpΔT, but the rise in internal energy is still nCvΔT.

  • An isothermal answer to a sudden change

    A sudden change leaves no time for heat to flow, so it is adiabatic. The PV = constant answer is always among the options.

  • Dividing by γ

    Adiabatic work is nR(T₁ − T₂)/(γ − 1). Dividing by γ gives a much smaller value that is often an option.

  • Celsius in an efficiency

    Between 327 °C and 27 °C, η = 1 − 300/600, not 1 − 27/327. Only a temperature difference may stay in °C.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Thermodynamics notes

Drill every Thermodynamics question

125 questions from the bank, across 6 subtopics.

Drill the 125 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

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