A LevelPhysicsOCRRevision Notes5. Newtonian World & AstrophysicsKinetic Theory of GasesInternal Energy of an Ideal Gas

Internal Energy of an Ideal Gas (OCR A Level Physics): Revision Note

Exam code: H556

Katie M

Written by: Katie M

Updated on

Internal Energy of an Ideal Gas

  • The internal energy of an ideal gas is defined as:

The total kinetic energy of all the particles inside the gas

  • This is because one of the assumptions of an ideal gas states:

    • Electrostatic forces between particles in the gas are negligible except during collisions

    • So, there is no electrostatic potential energy in an ideal gas

  • Therefore, the internal energy is due to the kinetic energy only

Change in internal energy, downloadable AS & A Level Physics revision notes

As the container is heated up, the gas molecules move faster with higher kinetic energy and therefore higher internal energy

  • Change in internal energy, ΔU is equal to the total kinetic energy, EK of all the particles 

increment U space equals space E subscript straight K space equals space 1 half N m c with italic bar on top squared space equals space space 3 over 2 N k increment T

  • Where:

    • EK = total kinetic energy (J)

    • m = mass of one molecule (kg)

    • c with bar on top squared = mean square speed of a molecule (m2 s-2)

    • k = Boltzmann constant

    • T = temperature of the gas (K)

    • N = number of molecules

  • This equation shows that doubling the temperature will also double the internal energy of the particles

increment U space equals space 3 over 2 N k increment T

3 over 2 N k left parenthesis 2 T right parenthesis space equals space 6 over 2 N k T space equals space 3 N k T space equals space 2 U

Examiner Tips and Tricks

For a real gas, internal energy is defined as the sum of the kinetic and potential energies of the particles. But for an ideal gas, make sure your definition only refers to kinetic energy. In an exam, you would lose marks for implying there is potential energy (or any other energy) added to the kinetic energy.

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.