Average Kinetic Energy of a Molecule (SL IB Physics)

• 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