What is the First Law of Thermodynamics?
The first law of thermodynamics is the principle of energy conservation applied to thermodynamic systems: energy cannot be created or destroyed, only converted between heat, work and internal energy. It is the foundation for analyzing engines, refrigerators and every energy-conversion process.
The first law states that the change in a system's internal energy equals the heat added to it minus the work done by it: ΔU = Q − W.
- 1↓Define the system boundaryDecide exactly what is inside the system and what is surroundings.
- 2↓Measure heat QDetermine heat flowing into (positive) or out of (negative) the system.
- 3↓Measure work WDetermine work done by (positive) or on (negative) the system.
- 4↓Compute ΔU = Q − WCombine heat and work to find the net change in internal energy.
- 5Interpret the resultΔU > 0 means internal energy increased; ΔU < 0 means it decreased.
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Step-by-step worked examples
A gas absorbs 500 J of heat and does 200 J of work on its surroundings as it expands. Find the change in internal energy.
ΔU = Q − W ΔU = 500 − 200 ΔU = 300 J
A gas is compressed adiabatically (Q = 0) and 150 J of work is done ON the gas (so W = −150 J by the gas). Find ΔU.
ΔU = Q − W ΔU = 0 − (−150) ΔU = 150 J
During one stroke of an engine cycle, 1000 J of heat is added and the gas does 650 J of work on the piston. Find ΔU for that stroke.
ΔU = Q − W ΔU = 1000 − 650 ΔU = 350 J
Flashcards
Quick quiz
Q1.What does the first law of thermodynamics state?
Q2.A system absorbs 400 J of heat and does 150 J of work. What is ΔU?
Q3.In an adiabatic process, Q = 0. What follows?
Q4.Over one full thermodynamic cycle, ΔU equals:
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Common mistakes
Confusing heat (Q) and work (W) as the same form of energy transfer. — Correct: Heat transfers energy due to a temperature difference; work transfers energy through a mechanical force acting through a distance — they are distinct.
Forgetting sign conventions and adding Q and W instead of subtracting. — Correct: With work done BY the system taken as positive, the correct relation is ΔU = Q − W, not Q + W.
Assuming ΔU = 0 for every process. — Correct: ΔU = 0 only over a complete cycle or in specific constant-internal-energy processes — not in general.
Treating Q and W as state functions like U. — Correct: Q and W depend on the path taken between states; only internal energy U is a true state function.
FAQ
What is the first law of thermodynamics?
It's the law of energy conservation for thermodynamic systems: ΔU = Q − W, where internal energy change equals heat added minus work done by the system.
What is the first law of thermodynamics formula?
ΔU = Q − W, with ΔU, Q and W all measured in joules (J).
What are some first law of thermodynamics examples?
A gas expanding in a piston, an adiabatic compression in an engine, a gas heated at constant volume, and a complete refrigeration cycle.
How do you calculate change in internal energy?
Subtract the work done by the system from the heat added to the system: ΔU = Q − W, using consistent sign conventions.