OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(e) the equation pV = 1/3 Nmc², where N is the number of particles (atoms…
Full specification wording
Ideal gases: (e) the equation pV = 1/3 Nmc², where N is the number of particles (atoms or molecules) and c² is the mean square speed
The kinetic theory equation pV = ⅓ N m c² relates the macroscopic pressure and volume of an ideal gas to the microscopic motion of its particles.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 6 of 10
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The kinetic theory equation pV = ⅓ N m c² relates the macroscopic pressure and volume of an ideal gas to the microscopic motion of its particles. Here N is the number of particles (atoms or molecules), m is the mass of one particle, and c² is the mean square speed of the particles. The equation assumes a large number of identical particles in random motion, with negligible volume and no intermolecular forces except during elastic collisions. It can be used to calculate pressure, volume, number of particles, or mean square speed. In multiple-choice questions, you may be asked to rearrange the equation, identify the meaning of each symbol, or calculate a quantity given the others.
What earns the marks
- State the equation pV = ⅓ N m c².
- Define N as the number of particles (atoms or molecules).
- Define m as the mass of one particle.
- Define c² as the mean square speed of the particles.
- Rearrange the equation to solve for pressure, volume, number of particles, or mean square speed.
- Recognise that c² is the average of the squares of the speeds, not the square of the average speed.
Common mistakes and how to put them right
Confusing c² with the square of the mean speed.
Put it right: c² is the mean of the squares of the speeds.
Using the total mass of gas instead of the mass of a single particle in the equation.
Forgetting the factor of ⅓ in the equation.
Using the equation for non-ideal gases where intermolecular forces are significant.
Exam tips
- Check that all quantities are in SI units: pressure in Pa, volume in m³, mass in kg, speed in m s⁻¹.
- When rearranging, isolate the required variable carefully, remembering the factor ⅓.
- In multiple-choice questions, look for distractors that omit the ⅓ or confuse mean square speed with square of mean speed.
Try the lesson
The start of the Ideal gases: (e) the equation pV = 1/3 Nmc², where N is the number of particles (atoms or molecules) and c² is the mean square speed lesson, made from checked teaching notes for this specification point.
Listen
The kinetic theory equation pV = ⅓ N m c² relates the macroscopic pressure and volume of an ideal gas to the microscopic motion of its particles. Here N is the number of particles (atoms or molecules), m is the mass of one particle, and c² is the mean square speed of the particles. The equation assumes a large number of identical particles in random motion, with negligible volume and no intermolecular forces except during elastic collisions. It can be used to calculate pressure, volume, number of particles, or mean square speed. In multiple-choice questions, you may be asked to rearrange the equation, identify the meaning of each symbol, or calculate a quantity given the others. A strong answer earns marks for these points. State the equation pV = ⅓ N m c². Define N as the number of particles (atoms or molecules). Define m as the mass of one particle. Define c² as the mean square speed of the particles. Exam tip: Check that all quantities are in SI units: pressure in Pa, volume in m³, mass in kg, speed in m s⁻¹.
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Key words
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Mean square speed
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Ideal gas assumptions
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N
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See every definition
- Mean square speed
- The average of the squares of the speeds of the particles, not the square of the average speed.
- Ideal gas assumptions
- A large number of identical particles in random motion, with negligible volume and no intermolecular forces except during elastic collisions.
- N
- The number of particles (atoms or molecules).
Label the diagram
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1Box 1
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