Thermodynamics Laws & Specific Heats of Gases

Ten connected videos that build thermodynamics layer by layer: temperature and the zeroth law, the first law and P–V diagrams, specific heats, every standard process, then engines, refrigerators and the second law. Every subtopic has a worked example in the video and on its page; the formula sheet, revision sheet and practice set cover the whole chapter.

Learning path · Formula sheet · Practice set

Print and revise: Revision sheet (PDF) · Formula sheet (PDF, one page)

Two blocks in contact settling to one temperature.

Part 1 of 10

Thermal Equilibrium and the Zeroth Law

Explain thermal equilibrium and the zeroth law, and why it lets us define temperature before the first and second laws.

Thermal equilibrium · Zeroth law of thermodynamics · Temperature and thermometers

A gas in a cylinder with a piston, heated by a flame.

Part 2 of 10

First Law of Thermodynamics

Use ΔQ = ΔU + ΔW with the right signs, and compute heat (Q = nCΔT), work (W = ∫P dV) and internal-energy change (ΔU = (f/2)nRΔT) for a gas.

First law ΔQ = ΔU + ΔW · Molar specific heat · Work done by a gas W = ∫P dV · Change in internal energy

A curve between two states on a P–V diagram, area shaded.

Part 3 of 10

Indicator Diagrams, State Variables and Cycles

Read P–V diagrams: states, paths and work as area; tell state variables from path variables; and find the net work and heat of clockwise and anticlockwise cycles.

Indicator (P–V) diagram · State and path variables · Cyclic processes · Positive and negative cycles

Part 4 of 10

Molar Specific Heats: Cv, Cp and γ

Derive C_v = (f/2)R and Mayer's relation C_p = C_v + R, find γ = (f + 2)/f, and combine gases into an equivalent γ for a mixture.

C_v = (f/2)R · Mayer's relation C_p − C_v = R · Ratio γ = C_p/C_v · γ of a gas mixture

Vertical line on a P–V diagram between two isotherms.

Part 5 of 10

Isochoric, Isobaric and Isothermal Processes

Find Q, W and ΔU for isochoric, isobaric and isothermal processes and draw each on a P–V diagram.

Isochoric process · Isobaric process · Isothermal process W = nRT ln(V₂/V₁)

Part 6 of 10

Adiabatic Process

Derive PV^γ = constant, compare the adiabat with the isotherm, and use the adiabatic work and temperature relations, including adiabatic vs isothermal bulk modulus.

Adiabatic process Q = 0 · PV^γ and TV^(γ−1) constant · Adiabat steeper than isotherm · Adiabatic work · Bulk modulus P and γP

A box with gas on the left half and vacuum on the right.

Part 7 of 10

Free Expansion of a Gas

Show that free expansion into a vacuum has Q = 0, W = 0 and ΔU = 0, and use Boyle's law for the end states of an ideal gas.

Free expansion into a vacuum · Q = W = ΔU = 0 · Irreversible process

Polytropic curves for n = 0, 1, gamma and infinity through one point.

Part 8 of 10

Polytropic Process

Treat every standard process as PVⁿ = constant, find the molar heat capacity C = R/(γ − 1) + R/(1 − n), and compare slopes on a P–V diagram.

Polytropic process PVⁿ = constant · C = R/(γ − 1) + R/(1 − n) · Slope n times the isotherm's

Table comparing reversible and irreversible processes.

Part 9 of 10

Reversible Processes, Heat Engines and Refrigerators

Explain reversible processes, analyse heat engines (W = Q₁ − Q₂, η = W/Q₁) and refrigerators (COP = Q₂/W).

Reversible and irreversible processes · Heat engine · Thermal efficiency · Refrigerator and COP

Engine diagram with no cold reservoir flow, crossed out.

Part 10 of 10

Second Law and the Carnot Cycle

State the Kelvin–Planck and Clausius forms of the second law, and use the Carnot cycle's efficiency η = 1 − T₂/T₁ as the limit for any engine.

Kelvin–Planck statement · Clausius statement · Carnot cycle · Carnot efficiency η = 1 − T₂/T₁