Thermal Energy

Physics

Thermal energy is the total kinetic energy of all the moving particles in a substance; it depends on temperature, mass, and material.

Visualization

Definition

Thermal energy is the energy inside something that comes from its tiny particles jiggling and bouncing around; the faster they move, the more thermal energy the object has. It is the total kinetic energy of all the atoms and molecules in a substance, and it depends on three things: the temperature (average particle energy), the number of particles (mass), and the type of material, so a large object at a low temperature can hold more thermal energy than a small object at a high temperature. At the microscopic level it is the internal energy associated with random particle motion, including translational, rotational, and vibrational modes; for an ideal monatomic gas it is $U = \tfrac{3}{2}NkT$, proportional to absolute temperature. The energy needed to change a substance's temperature is $Q = mc\,\Delta T$, where $c$ is specific heat capacity. Thermal energy is the destination of dissipative processes such as friction and electrical resistance.

Example

A cup of hot cocoa has more thermal energy than the same cup of cold milk, because its particles are moving faster. A bathtub of warm water at $40^\circ\text{C}$ holds far more thermal energy than a cup of boiling tea at $100^\circ\text{C}$, because the tub contains thousands of times more water molecules. Warming $2\ \text{kg}$ of water from $20^\circ\text{C}$ to $80^\circ\text{C}$ requires $Q = 2 \times 4186 \times 60 \approx 502{,}000\ \text{J}$. The same energy would heat $2\ \text{kg}$ of copper ($c = 385\ \text{J/(kg}\cdot^\circ\text{C)}$) by $652^\circ\text{C}$, which is why water is such an effective coolant.

Key Insight

Even ice has thermal energy; its particles are moving slowly, but they are still moving, and only at absolute zero would they nearly stop. Temperature and thermal energy are not the same: a spark from a sparkler is thousands of degrees but carries so little thermal energy that it does not burn you. Water's high specific heat is why coastal cities have mild climates and why your body uses sweat to dump heat. Storing a lot of energy per degree makes water a thermal buffer.