OCR A Level Physics

Revision Notes

A LevelPhysicsOCRRevision Notes5. Newtonian World & Astrophysics5.3 Kinetic Theory of Gases5.3.5 Internal Energy of an Ideal Gas

5.3.5 Internal Energy of an Ideal Gas

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Internal Energy of an Ideal Gas

  • The internal energy of a gas is defined as:

The sum of the kinetic and potential energies of the particles inside the gas

  • 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
  • All the internal energy is due to the kinetic energy of the particles

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 

bold increment bold italic U bold space bold equals bold italic E subscript bold K bold equals bold 1 over bold 2 bold italic N bold italic m stack bold c to the power of bold 2 with bold bar on top bold equals bold space bold 3 over bold 2 bold italic N bold italic k bold increment bold italic T

  • Where:
    • EK = total kinetic energy (J)
    • m = mass of one molecule (kg)
    • stack c squared with bar on top = 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

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

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