16.1 Internal Energy

Internal Energy ( $U$)

Sum of a random distribution of kinetic and potential energies associated with the particles of a system.

Kinetic Energy ( $E_k$)

• Associated with the random motion (translational, rotational vibrational) of the molecules.
• A rise in thermodynamic temperature is directly related to an increase in the mean kinetic energy of molecules: $E_k=\frac{3}{2}kT$ $E_k\propto T$

Potential Energy ( $E_p$)

• Associated with the intermolecular forces between the molecules.
• It varies with the separation of the particles.

Internal Energy in Water

Internal Energy of an Ideal Gas

Internal Energy of an Ideal Gas

Total kinetic energy associated with the random motion of molecules plus total potential energy of molecules but potential energy is zero due to absence of intermolecular forces.

Internal Energy of an Ideal Gas

One of the core assumptions of the kinetic theory of ideal gases is that there are no intermolecular forces between the molecules. Because there are no intermolecular forces, the molecules have zero potential energy. Therefore, the internal energy of an ideal gas is purely equal to the total kinetic energy of its molecules.

Because internal energy in an ideal gas is solely kinetic, and mean kinetic energy is directly proportional to thermodynamic temperature ($E_k=\frac{3}{2}kT$), we can state:

$\Delta U\propto \Delta T$

For an ideal gas, the change in internal energy is directly proportional to the change in thermodynamic temperature. If the temperature doesn’t change (isothermal), the internal energy doesn’t change ($\Delta U=0$).