The first law of thermodynamics Cambridge International AS & A Level Physics revision
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In plain words
There are two ways to raise the internal energy of a gas: heat it, or squash it. Pump up a bicycle tyre and the pump gets warm, although nobody heated it: you did work on the gas. The first law of thermodynamics is just the conservation of energy, keeping count of both.
4 things to know
- When the volume of a gas changes at constant pressure, the work done is W = pΔV. A gas that expands does work on its surroundings. A gas that is compressed has work done on it.
- The first law: ΔU = q + W. The increase in internal energy equals the energy supplied by heating plus the work done on the system.
- Signs: q is positive when the system is heated and negative when it loses thermal energy. W is positive when work is done on the gas (compression) and negative when the gas does work (expansion).
- The internal energy of an ideal gas depends only on its temperature, so if the temperature doesn't change, ΔU = 0.
Worked example
A gas is given 500 J by heating while it expands at a constant pressure of 1.0 × 10⁵ Pa from 2.0 × 10⁻³ m³ to 3.5 × 10⁻³ m³. Find the change in its internal energy.
- Work done by the gas = pΔV = 1.0 × 10⁵ × 1.5 × 10⁻³ = 150 J.
- The gas did the work, so the work done on it is W = −150 J.
- ΔU = q + W = 500 − 150 = +350 J.
Tips and tricks
- Decide the sign of q and of W before you put any numbers in.
- Expansion: W is negative. Compression: W is positive.
It lands in your notebook with its questions as flashcards.
The first law of thermodynamics: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
In ΔU = q + W, what is W?
Work done on the gas raises its internal energy.
A gas is compressed. What is the sign of W, the work done on the gas?
Compressing a gas does work on it.
A gas expands by 2.0 × 10⁻³ m³ at a constant pressure of 1.0 × 10⁵ Pa. How much work does the gas do?
W = pΔV.
A gas is heated in a sealed, rigid container. How much work is done?
The volume doesn't change.
An ideal gas is compressed quickly, so no thermal energy can escape. What happens to its temperature?
The work done on it increases its internal energy.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
The first law of thermodynamics
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
A gas expands by 4.0 × 10⁻⁴ m³ at a constant pressure of 2.0 × 10⁵ Pa. Find the work done by the gas.[2]
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80 J.
300 J of work is done in compressing a gas, and 120 J of thermal energy leaves it. Find the change in its internal energy.[3]
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+180 J. ΔU = (−120) + 300.
An ideal gas expands at constant temperature and does 250 J of work. Find the thermal energy supplied to it.[2]
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250 J. The temperature is constant, so ΔU = 0 and q = −W = 250 J.
Answers: The first law of thermodynamics
- 1. 80 J.
- 2. +180 J. ΔU = (−120) + 300.
- 3. 250 J. The temperature is constant, so ΔU = 0 and q = −W = 250 J.