OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Ideal gases: (i) internal energy of an ideal gas.
The internal energy of an ideal gas is the total kinetic energy of its molecules, because ideal-gas molecules are modelled as having no intermolecular potential energy.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 10 of 10
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The internal energy of an ideal gas is the total kinetic energy of its molecules, because ideal-gas molecules are modelled as having no intermolecular potential energy. For N molecules each with mean translational kinetic energy 3/2 kT, the internal energy is U = N × 3/2 kT = 3/2 NkT. Since NkT = pV, this can also be written U = 3/2 pV. Internal energy therefore depends only on the temperature (or on the product pV) and on the number of molecules, not on the type of gas. Doubling the thermodynamic temperature of a fixed amount of ideal gas doubles its internal energy.
What earns the marks
- Defines the internal energy of an ideal gas as the total kinetic energy of its molecules.
- States that ideal-gas molecules have negligible intermolecular potential energy, so no potential term is included.
- Derives or applies U = 3/2 NkT for N molecules.
- Uses NkT = pV to write U = 3/2 pV where convenient.
- Explains that internal energy depends on temperature and number of molecules, not on the identity of the gas.
Common mistakes and how to put them right
Including intermolecular potential energy in the internal energy of an ideal gas.
Put it right: The ideal-gas model treats it as negligible, leaving kinetic energy only.
Using U = 3/2 nRT with N.
Put it right: Use NkT for molecules or nRT for moles, matching the count to the constant.
Assuming internal energy depends on pressure or volume separately.
Put it right: For a fixed number of molecules it depends only on temperature.
Forgetting the 3/2 factor and writing U = NkT.
Put it right: Each molecule contributes 3/2 kT on average.
Exam tips
- State clearly that the ideal-gas model has no intermolecular potential energy before writing U = 3/2 NkT.
- Choose NkT or nRT according to whether the question counts molecules or moles.
- If p and V are given, use U = 3/2 pV to avoid needing the temperature.
- Explain changes in internal energy in terms of temperature changes for a fixed amount of gas.
Try the lesson
The start of the Ideal gases: (i) internal energy of an ideal gas. lesson, made from checked teaching notes for this specification point.
Listen
The internal energy of an ideal gas is the total kinetic energy of its molecules, because ideal-gas molecules are modelled as having no intermolecular potential energy. For N molecules each with mean translational kinetic energy 3/2 kT, the internal energy is U = N × 3/2 kT = 3/2 NkT. Since NkT = pV, this can also be written U = 3/2 pV. Internal energy therefore depends only on the temperature (or on the product pV) and on the number of molecules, not on the type of gas. Doubling the thermodynamic temperature of a fixed amount of ideal gas doubles its internal energy. A strong answer earns marks for these points. Defines the internal energy of an ideal gas as the total kinetic energy of its molecules. States that ideal-gas molecules have negligible intermolecular potential energy, so no potential term is included. Derives or applies U = 3/2 NkT for N molecules. Uses NkT = pV to write U = 3/2 pV where convenient. A common slip: Including intermolecular potential energy in the internal energy of an ideal gas. Instead, the ideal-gas model treats it as negligible, leaving kinetic energy only. Exam tip: State clearly that the ideal-gas model has no intermolecular potential energy before writing U = 3/2 NkT.
Key words
Say what each word means before you turn the card.
Internal energy and the ideal-gas model
Try answering aloud or in your head before turning the card.
Kinetic energy of molecules
Try answering aloud or in your head before turning the card.
Temperature as a measure of internal energy
Try answering aloud or in your head before turning the card.
Assumptions of ideal-gas behaviour
Try answering aloud or in your head before turning the card.
See every definition
- Internal energy and the ideal-gas model
- The total kinetic energy of the molecules of an ideal gas, since the ideal-gas model treats intermolecular potential energy as negligible.
- Kinetic energy of molecules
- Each molecule has a mean translational kinetic energy of 3/2 kT, so for N molecules the total is U = 3/2 NkT.
- Temperature as a measure of internal energy
- Internal energy depends only on the temperature and on the number of molecules, not on the type of gas, so doubling the thermodynamic temperature of a fixed amount of ideal gas doubles its internal energy.
- Assumptions of ideal-gas behaviour
- Ideal-gas molecules are modelled as having no intermolecular potential energy, so no potential term is included in the internal energy.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Ideal gases: (i) internal energy of an ideal gas.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge