Internal energy and absolute zero

Internal energy

The internal energy of a body is the sum of the randomly distributed kinetic and potential energies of its molecules.

• Heating a body, or doing work on it, increases its internal energy.
• A temperature rise means the molecules' mean kinetic energy has increased.
• A change of state at constant temperature increases the potential energy (energy breaks or weakens the bonds between molecules).

Absolute zero

Absolute zero is the lowest possible temperature, 0 K = -273 °C (-273.15 °C precisely). At absolute zero, the molecules have their minimum possible kinetic energy, and so the substance has its minimum internal energy.

• To convert: T (K) = θ (°C) + 273
• A change of 1 K equals a change of 1 °C.

Temperature and kinetic energy

The mean kinetic energy of the molecules is proportional to the absolute temperature T. Doubling T in kelvin doubles the mean kinetic energy; doubling a Celsius temperature does not. For an ideal gas there are no intermolecular forces, so its internal energy is entirely kinetic.

Worked example

A gas is heated from 27 °C to 327 °C. By what factor does the mean kinetic energy of its molecules increase?

1. T_1 = 27 + 273 = 300 K
2. T_2 = 327 + 273 = 600 K
3. Mean E_k is proportional to T: 600 / 300 = 2

Answer: It doubles

Check yourself

1. Convert 25 °C to kelvin.
   Show answer

   298 K. T = 25 + 273 = 298 K.

2. Liquid nitrogen boils at 77 K. Convert this to °C.
   Show answer

   -196 °C. θ = 77 - 273 = -196 °C.

3. A gas is heated from 7 °C to 147 °C. By what factor does the mean kinetic energy of its molecules increase?
   Show answer

   1.5. 280 K to 420 K, so the mean E_k increases by a factor of 420 / 280 = 1.5.

4. What is the internal energy of a substance?
   • The sum of the randomly distributed kinetic and potential energies of its molecules
   • The kinetic energy of the substance as a whole
   • The thermal energy supplied to it
   • The energy stored in its nuclei
   Show answer

   The sum of the randomly distributed kinetic and potential energies of its molecules. Internal energy is about the random motion and positions of the molecules.

5. What is true at absolute zero?
   • All molecules move at the same high speed
   • The substance has maximum internal energy
   • The molecules have their minimum possible kinetic energy
   • The temperature is 0 °C
   Show answer

   The molecules have their minimum possible kinetic energy. 0 K is the temperature at which the internal energy is at its minimum.

6. Water boils at constant temperature. What happens to its internal energy?
   • It increases, because the molecules' potential energy increases
   • It stays the same, because the temperature is constant
   • It decreases, because molecules escape
   • It increases, because the molecules' mean kinetic energy increases
   Show answer

   It increases, because the molecules' potential energy increases. Energy is absorbed to separate the molecules, raising their potential energy.

7. Why is the internal energy of an ideal gas entirely kinetic?
   • Its molecules do not move
   • It is always at absolute zero
   • There are no forces between its molecules, so they have no potential energy
   • Its molecules have no mass
   Show answer

   There are no forces between its molecules, so they have no potential energy. Potential energy comes from intermolecular forces, which an ideal gas does not have.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.