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📘 Lesson 7 of 10 · Thermodynamics

⚖️ First Law of Thermodynamics

The first law of thermodynamics is really just energy conservation applied to heat and work — energy can change form or move around, but it can never be created or destroyed.

Course progress: 70%

01 Key Concepts

The First Law Statement

The change in a system's internal energy equals the heat added to the system minus the work done BY the system: delta_U = Q - W.

Internal Energy (U)

The total kinetic and potential energy of all the particles within a system -- roughly, the system's total 'thermal content'.

Sign Conventions

Q is positive when heat is added to the system; W is positive when the system does work on its surroundings (like an expanding gas pushing a piston).

Special Cases

Isothermal (constant temperature, so delta_U=0, meaning Q=W). Adiabatic (no heat exchange, so Q=0, meaning delta_U=-W). Isochoric (constant volume, so W=0, meaning delta_U=Q).

Why the First Law Matters

It guarantees that no process -- no engine, no chemical reaction, no biological system -- can create energy from nothing or destroy it; energy is always conserved, just converted.

02 Key Formulas

03 Solved Examples

Example 1 A gas absorbs 500 J of heat and does 200 J of work on its surroundings. Find the change in internal energy.
  1. Apply delta_U = Q - W = 500 - 200.
Answer: 300 J
Example 2 A gas has 300 J of work done ON it (compression) with no heat exchange (adiabatic). Find the change in internal energy.
  1. Work done ON the system is negative W (since W is defined as work done BY the system): W = -300 J.
  2. Q = 0 (adiabatic).
  3. delta_U = Q - W = 0 - (-300).
Answer: 300 J (internal energy increases, since compression adds energy without heat loss)
Example 3 In an isothermal process, why does Q equal W exactly?
  1. Isothermal means constant temperature, and internal energy for an ideal gas depends only on temperature.
  2. So delta_U = 0, and rearranging delta_U=Q-W gives 0=Q-W, meaning Q=W.
Answer: Because delta_U=0 at constant temperature, the first law reduces to Q=W

04 Practice Questions

1A gas absorbs 800 J of heat and does 300 J of work. Find delta_U.
500 J
2A gas releases 200 J of heat and has 100 J of work done on it. Find delta_U. (Q=-200, W=-100)
delta_U=-200-(-100)=-100 J
3What does 'adiabatic' mean?
No heat exchange occurs (Q=0)
4What does 'isochoric' mean?
Constant volume (so no work is done, W=0)
5What fundamental principle does the first law of thermodynamics represent?
Conservation of energy

📄 First Law of Thermodynamics — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

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