What does this Thermodynamics cheat sheet cover?

It has 10 sections: State Variables, First Law, PV Work, Process Types, Heat Capacity, Second Law, Carnot Engines, Refrigerators, Free Energy and Phase Change. Together they cover the topics a typical Thermodynamics exam tests, including ideal gas law, first law of thermodynamics, work in PV processes and isothermal, isobaric, isochoric, adiabatic processes.

Is the thermodynamics cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Thermodynamics cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 2 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Thermodynamics sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Physics & EngineeringThermodynamics

Thermodynamics Cheat Sheet — 1-page PDF

Ideal gases, work/heat, laws, entropy, engines, free energies, phase changes. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

Make this from your notes Unlock the full sheet

The first part is free below. See pricing →

For a specific exam: Thermodynamics Final exam study sheet.

1 pageUS Letter
10 sections10 topics
Free previewfull sheet with Unlimited

Preview of the one-page Thermodynamics cheat sheet: Ideal gases, work/heat, laws, entropy, engines, free energies, phase changes — the whole course, one page

On the sheet

What’s on it

The topics a typical Thermodynamics exam tests, all on the one page.

Ideal gas law
First law of thermodynamics
Work in PV processes
Isothermal, isobaric, isochoric, adiabatic processes
Heat capacity
Second law and entropy
Carnot efficiency and heat engines
Refrigerators and COP
Gibbs and Helmholtz free energy
Phase changes

Free preview

The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01State Variables

Thermodynamic state: Macroscopic state fixed by variables like $P, V, T, n, U, S$ ; equilibrium state well-defined.
Ideal gas: Model with $P V = n R T$ ; molecules noninteracting except elastic collisions.

Ideal gas law

P V = n R T = N k_{B} T

$n$ moles, $N$ particles, $R = N_{A} k_{B}$ .

Moles

n = \frac{m}{M}

$m$ mass, $M$ molar mass.

Density form

P = ρ R_{spec} T

$R_{spec} = R / M$ .

Common state vars

Symbol	Meaning	Type
$P$	pressure	state
$V$	volume	state
$T$	temperature	state
$U$	internal energy	state
$S$	entropy	state

Watch out:Do not treat $Q$ or $W$ as state variables; path-dependent.

02PV Work

Adiabatic relations

T V^{γ - 1} = const, T^{γ} P^{1 - γ} = const

Same process.

Watch out:For irreversible paths, $W \neq = \int P_{gas} d V$ unless you know the actual external pressure path.

03Process Types

Standard processes

Process	Fixed	Key result	Work
Isothermal	$T$	$Δ U = 0$	$n R T ln (V_{f} / V_{i})$
Isobaric	$P$	$W = P Δ V$	$P Δ V$
Isochoric	$V$	$W = 0$	$0$
Adiabatic	$Q = 0$	$Q = 0$	from $Δ U$

Adiabatic work

W = - Δ U

Because $Q = 0$ .

Ideal gas $Δ U$

Δ U = n C_{V} Δ T

For ideal gas.

Enthalpy

H = U + P V

Useful for constant-pressure processes.

04Second Law

Entropy: State function measuring reversible heat flow: $d S = \frac{δ Q _{rev}}{T}$ .

Entropy change

Δ S = \int \frac{δ Q _{rev}}{T}

Any path, but use a reversible path to compute.

Clausius inequality

\oint \frac{δ Q}{T} \leq 0

Equality for reversible cycle.

Isothermal entropy

Δ S = n R ln (\frac{V _{f}}{V _{i}}) = n R ln (\frac{P _{i}}{P _{f}})

Reversible ideal gas.

Isochoric entropy

Δ S = n C_{V} ln (\frac{T _{f}}{T _{i}})

Ideal gas, $V$ constant.

Isobaric entropy

Δ S = n C_{P} ln (\frac{T _{f}}{T _{i}})

Ideal gas, $P$ constant.

05Carnot Engines

Heat engine: Cyclic device converting heat from hot reservoir to work.

Engine efficiency

η = \frac{W _{out}}{Q _{H}} = 1 - \frac{Q _{C}}{Q _{H}}

$Q_{H}$ absorbed from hot reservoir, $Q_{C}$ rejected to cold.

06Refrigerators

Ex.If $Q_{C} = 200 J$ and $W = 50 J$ , find $COP_{R}$ .

$COP_{R} = 200/50 = 4$ .

07Free Energy

Helmholtz free energy

F = U - T S

Useful at constant $T, V$ .

Gibbs free energy

G = H - T S = U + P V - T S

Useful at constant $T, P$ .

Spontaneity criteria

Δ F \leq 0 (T, V const), Δ G \leq 0 (T, P const)

Equality at equilibrium.

Differentials

d F = - S d T - P d V, d G = - S d T + V d P

From definitions and $d U = T d S - P d V$ for reversible change.

Equilibrium conditions

(\frac{\partial F}{\partial V})_{T} = - P, (\frac{\partial G}{\partial P})_{T} = V

State relations.

Watch out:At constant $T, P$ , use $Δ G$ for direction, not $Δ U$ .

Cheat sheet locked

Also on the full Thermodynamics sheet

8 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

First Law

First law
Internal energy U
Differential form
Quasistatic PV work
Closed cycle

PV Work

Isobaric work
Isochoric work
Isothermal ideal gas
Isothermal work
Adiabatic
Adiabatic reversible

Process Types

Ideal gas enthalpy

Heat Capacity

Heat capacity
Specific heat
Molar heats
Ideal gas identity
Gamma
Monatomic ideal gas
Diatomic ideal gas

Second Law

Second law

Carnot Engines

Carnot efficiency
Reversible engine
Carnot cycle

Refrigerators

Refrigerator
COP refrigerator
COP heat pump
Carnot COP
Engine vs refrigerator

Phase Change

Latent heat
Phase-change heat
Clapeyron equation
Clausius-Clapeyron
Phase change signs

Unlock the full sheet $4.99 a month or $19 a semester

Or make this from your own notes

FAQ

Questions

About the Thermodynamics sheet and making your own.

What does this Thermodynamics cheat sheet cover?: It has 10 sections: State Variables, First Law, PV Work, Process Types, Heat Capacity, Second Law, Carnot Engines, Refrigerators, Free Energy and Phase Change. Together they cover the topics a typical Thermodynamics exam tests, including ideal gas law, first law of thermodynamics, work in PV processes and isothermal, isobaric, isochoric, adiabatic processes.
Is the thermodynamics cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Thermodynamics cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 2 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Thermodynamics sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Keep going

All 40 sheets are in the sheet library.

Your course, your notes, one page.

Make this from your notes

Upload your own Thermodynamics slides or notes and get a study sheet in your course’s notation. Your first sheet needs no account, and a free account adds one more. See pricing