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Matter: Very Simple

Temperature, average energy per particle and internal energy

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on a particle's mean kinetic energy, kT as a rough measure, its value in joules and electronvolts, the internal energy of an ideal gas, and root mean square speeds.

What you need to know

Answer each one before you reveal it.

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Key term

How is the absolute temperature of a gas related to the energy of its particles?

Key term

Why is kT often used as a rough measure of the energy per particle?

Numbers

Calculate the value of kT at 300 K.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is the absolute temperature of a gas related to the energy of its particles?

    Model answer

    The average random kinetic energy of a particle is directly proportional to the absolute temperature.

  2. 2

    Give the expression for the mean kinetic energy of a particle in an ideal gas.

    Model answer

    It is 3/2 kT, where k is the Boltzmann constant and T the absolute temperature.

  3. 3

    Why is kT often used as a rough measure of the energy per particle?

    Model answer

    The factor of 3/2 is close to one, so kT gives the right order of magnitude and is good enough for an estimate.

  4. 4

    Calculate the value of kT at 300 K.

    Model answer

    kT = 1.38 × 10⁻²³ × 300 = 4.1 × 10⁻²¹ J.

  5. 5

    Express the value of kT at 300 K in electronvolts.

    Model answer

    It is 4.14 × 10⁻²¹ ÷ (1.60 × 10⁻¹⁹) ≈ 0.026 eV, about one fortieth of an electronvolt.

  6. 6

    Calculate the mean kinetic energy of a gas particle at 300 K.

    Model answer

    It is 3/2 kT = 1.5 × 1.38 × 10⁻²³ × 300 = 6.2 × 10⁻²¹ J.

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