What is k in the ideal gas equation, and what is its value and unit?

It is the Boltzmann constant, equal to 1.38 × 10⁻²³ J K⁻¹.

What is meant by an ideal gas?

It is a gas that obeys pV = NkT at all pressures, volumes and temperatures, having molecules of negligible volume with no forces between them except during collisions.

How many molecules are there in 2.0 × 10⁻³ m³ of gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K?

N = pV/kT = (1.0 × 10⁵ × 2.0 × 10⁻³)/(1.38 × 10⁻²³ × 300) = 4.8 × 10²² molecules.

How are pV = ⅓Nm⟨c²⟩ and pV = NkT combined to relate molecular kinetic energy to temperature?

Equating the two right-hand sides gives ⅓Nm⟨c²⟩ = NkT, so m⟨c²⟩ = 3kT, and halving both sides gives ½m⟨c²⟩ = (3/2)kT.

What does the result ½m⟨c²⟩ = (3/2)kT tell you about gases?

The mean translational kinetic energy of a molecule depends only on the absolute temperature, and is the same for any ideal gas at that temperature.

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Thermodynamics

The ideal gas equation and molecular kinetic energy

1 thing to know
Papers 2 and 3

Overview

Recall questions on pV = NkT and the Boltzmann constant, combining it with the kinetic theory equation, and comparing two gases held at the same temperature.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

What is the ideal gas equation in terms of the number of molecules, and what is k, its value and its unit?

Questions from this subtopic

Each one with the model answer underneath.

1
State the ideal gas equation written in terms of the number of molecules:
Model answer
The equation is pV = NkT.
2
What is k in the ideal gas equation, and what is its value and unit?
Model answer
It is the Boltzmann constant, equal to 1.38 × 10⁻²³ J K⁻¹.
3
What is meant by an ideal gas?
Model answer
It is a gas that obeys pV = NkT at all pressures, volumes and temperatures, having molecules of negligible volume with no forces between them except during collisions.
4
How many molecules are there in 2.0 × 10⁻³ m³ of gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K?
Model answer
N = pV/kT = (1.0 × 10⁵ × 2.0 × 10⁻³)/(1.38 × 10⁻²³ × 300) = 4.8 × 10²² molecules.
5
How are pV = ⅓Nm⟨c²⟩ and pV = NkT combined to relate molecular kinetic energy to temperature?
Model answer
Equating the two right-hand sides gives ⅓Nm⟨c²⟩ = NkT, so m⟨c²⟩ = 3kT, and halving both sides gives ½m⟨c²⟩ = (3/2)kT.
6
What does the result ½m⟨c²⟩ = (3/2)kT tell you about gases?
Model answer
The mean translational kinetic energy of a molecule depends only on the absolute temperature, and is the same for any ideal gas at that temperature.

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