Average Kinetic Energy of a Molecule (DP IB Physics)

Average Kinetic Energy of a Molecule

• We think of an ideal gas as molecules that collide elastically in random motion

• When the molecules collide, momentum and energy are conserved

  • We assume that, when the molecules are not in contact, no forces act between them

• This means they have no potential energy

  • Therefore, the internal energy U of an ideal, monatomic gas is equal to its average kinetic energy if the molecules are far enough apart

• The average kinetic energy, E_k for one molecule is equal to:

• Where:

  • E_k = average kinetic energy of one molecule (J)

  • v = mean square speed of one molecule (m s^–1)

  • m = mass of one molecule (kg)

  • k_B = Boltzmann constant

  • T = temperature of the gas (K)

• A consequence of this equation is that a greater gas temperature means a greater average kinetic energy of the particles

• Since the total internal energy is the total kinetic energy, the internal energy of a gas U is defined as:

• Where:

  • U = internal energy (J)

  • N = number of molecules

• The relation to the amount of substance is:

• Where:

  • n = number of moles

  • R = ideal gas constant

• When heat is transferred to a fixed volume of gas, the internal energy increases and hence, so does the temperature, since the equations show that

• This is only relevant for monatomic gases. Examples include:
  

  • Helium

  • Neon

  • Argon

• A monatomic (one atom) molecule only has translational energy, whilst a diatomic (two-atom) molecule has both translational and rotational energy

A diatomic molecule has both rotational and translational kinetic energy