AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Appreciation that for an ideal gas internal energy is kinetic energy of…
Full specification wording
Molecular kinetic theory model (A-level only): Appreciation that for an ideal gas internal energy is kinetic energy of the atoms.
An ideal gas is a model in which molecules are treated as point particles with negligible volume and no intermolecular forces except during instantaneous elastic collisions.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 5 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
An ideal gas is a model in which molecules are treated as point particles with negligible volume and no intermolecular forces except during instantaneous elastic collisions. Because there are no attractive or repulsive forces between molecules, there is no potential energy associated with their separation. Therefore the internal energy of an ideal gas is entirely the kinetic energy of its atoms or molecules. For a monatomic ideal gas, the mean kinetic energy per atom is (3/2)kT, where k is the Boltzmann constant and T is thermodynamic temperature. For N atoms, total internal energy U = (3/2)NkT, which also equals (3/2)nRT for n moles. This explains why the internal energy of an ideal gas depends only on its temperature, not on its volume or pressure.
What earns the marks
- State that an ideal gas has no intermolecular potential energy because intermolecular forces are negligible except during collisions.
- Identify the internal energy of an ideal gas as the total kinetic energy of its atoms or molecules.
- Use the relationship between mean molecular kinetic energy and thermodynamic temperature, for example (3/2)kT per atom for a monatomic gas.
- Explain that internal energy depends only on temperature for a fixed amount of ideal gas, not on volume or pressure.
- Apply U = (3/2)NkT or U = (3/2)nRT to calculate internal energy when N or n and T are known.
Common mistakes and how to put them right
Including potential energy in the internal energy of an ideal gas.
Put it right by stating that ideal-gas molecules have no potential energy because intermolecular forces are negligible.
Using Celsius temperature in kinetic energy calculations.
Put it right by converting to kelvin using T/K = θ/°C + 273.15.
Assuming internal energy depends on volume or pressure.
Put it right by explaining that for an ideal gas at fixed amount, internal energy is a function of temperature alone.
Exam tips
- Always convert temperatures to kelvin before using kT or RT.
- When asked to explain, link the absence of intermolecular forces directly to the absence of potential energy, then to kinetic energy only.
- Quote the equation you use and define each symbol, especially N, n, k and R.
Try the lesson
The start of the Molecular kinetic theory model (A-level only): Appreciation that for an ideal gas internal energy is kinetic energy of the atoms. lesson, made from checked teaching notes for this specification point.
Have a go first
For an ideal gas, what is the internal energy of the gas?
Listen
An ideal gas is a model in which molecules are treated as point particles with negligible volume and no intermolecular forces except during instantaneous elastic collisions. Because there are no attractive or repulsive forces between molecules, there is no potential energy associated with their separation. Therefore the internal energy of an ideal gas is entirely the kinetic energy of its atoms or molecules. For a monatomic ideal gas, the mean kinetic energy per atom is (3/2)kT, where k is the Boltzmann constant and T is thermodynamic temperature. For N atoms, total internal energy U = (3/2)NkT, which also equals (3/2)nRT for n moles. This explains why the internal energy of an ideal gas depends only on its temperature, not on its volume or pressure. A strong answer earns marks for these points. State that an ideal gas has no intermolecular potential energy because intermolecular forces are negligible except during collisions. Identify the internal energy of an ideal gas as the total kinetic energy of its atoms or molecules. Use the relationship between mean molecular kinetic energy and thermodynamic temperature, for example (3/2)kT per atom for a monatomic gas. Explain that internal energy depends only on temperature for a fixed amount of ideal gas, not on volume or pressure. A common slip: Including potential energy in the internal energy of an ideal gas. Instead, stating that ideal-gas molecules have no potential energy because intermolecular forces are negligible. Exam tip: Always convert temperatures to kelvin before using kT or RT.
Key words
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Internal energy of an ideal gas
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Mean molecular kinetic energy
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Total internal energy
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Dependence of internal energy
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See every definition
- Internal energy of an ideal gas
- Entirely the kinetic energy of its atoms or molecules, because there is no potential energy associated with their separation.
- Mean molecular kinetic energy
- For a monatomic ideal gas, (3/2)kT per atom, where k is the Boltzmann constant and T is thermodynamic temperature.
- Total internal energy
- For N atoms, U = (3/2)NkT, which also equals (3/2)nRT for n moles.
- Dependence of internal energy
- For an ideal gas it depends only on its temperature, not on its volume or pressure.
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