A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.

Thermodynamic Processes and the PV Diagram

College Depth 108 in the knowledge graph ☐ I know this ☆ Set as goal
1,207topics build on this
641prerequisites beneath it
See this on the map →
First Law of ThermodynamicsThe Ideal Gas Law→→Adiabatic ProcessesEntropy Changes in Thermodynamic Processes+15 more
PV-diagram thermodynamic-processes isothermal adiabatic isobaric isochoric

Core Idea

A thermodynamic process describes how a system transitions between equilibrium states, typically represented on a P-V (pressure-volume) diagram. The four idealized processes are: isothermal (constant T), adiabatic (Q = 0), isobaric (constant P), and isochoric or isovolumetric (constant V). Each traces a distinct curve on the PV diagram with a specific relationship between Q, W, and ΔU. Real engines and refrigerators approximate combinations of these idealized processes.

How It's Best Learned

Sketch all four process types on a single PV diagram starting from the same state. For each, identify which terms in ΔU = Q − W are zero and compute the others. This visual fluency on PV diagrams is essential for analyzing heat engines.

Common Misconceptions

Explainer

You already know the first law of thermodynamics — ΔU = Q − W — and the ideal gas law PV = nRT. Thermodynamic processes are where these two equations meet: they describe specific paths a gas can take as it changes state, and each path has a different signature for how Q, W, and ΔU relate to one another.

The PV diagram is the essential visual tool. Plot pressure on the vertical axis and volume on the horizontal axis. Every equilibrium state of a gas is a point on this diagram, and every quasi-static process is a curve connecting two points. The area under the curve on a PV diagram equals the work done by the gas during that process — a geometric fact you should internalize, because it makes comparing processes visual and immediate.

The four idealized processes each constrain one variable. In an isochoric (constant volume) process, the curve is a vertical line; no volume change means no work done, so ΔU = Q entirely. In an isobaric (constant pressure) process, the curve is horizontal; work W = PΔV, and both Q and ΔU are generally nonzero. In an isothermal process, temperature is fixed, so for an ideal gas ΔU = 0 and Q = W — heat flows in and is entirely converted to work. In an adiabatic process, no heat is exchanged (Q = 0), so any work done comes at the cost of internal energy: ΔU = −W. A gas expanding adiabatically cools, which is why diesel engines ignite fuel without a spark — the adiabatic compression heats the air enough to combust.

A common trap: students hear "isothermal" and assume no heat flows, or hear "adiabatic" and assume constant temperature. The names are clues: "iso-thermal" means same temperature; "a-diabatic" means no heat passage (from the Greek for "not passable"). Keep these definitions sharp. On a PV diagram, the adiabatic curve through any point is always steeper than the isothermal curve through the same point, because in an adiabatic expansion the temperature falls, causing pressure to drop faster than it would at constant temperature.

Real engines — the Carnot cycle, diesel engines, refrigerators — are sequences of these four idealized processes stitched together. The enclosed area on a PV diagram for a complete cycle equals the net work output of the engine. Building fluency with individual process types now is what makes heat engine analysis tractable later.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Center of Mass → Conservation of Linear Momentum → Elastic Collisions → Inelastic Collisions → Coefficient of Restitution → Collision Analysis and Real-World Applications → Two-Body Collisions in the Center-of-Mass Frame → Reduced Mass and Two-Body Problems → Kinematics in Two Dimensions → Projectile Motion → Circular Motion: Kinematics → Rotational Kinematics → Torque → Moment of Inertia → Rotational Kinetic Energy → The Work-Energy Theorem → Conservation of Mechanical Energy → First Law of Thermodynamics → Thermodynamic Processes and the PV Diagram

Longest path: 109 steps · 641 total prerequisite topics

Prerequisites (2)

Leads To (17)