14.1 Heat

Making connections: heat interpreted at the molecular level

What is observed as a change in temperature of two macroscopic objects in contact, such as a warm can of liquid and an ice cube, consists of the transfer of kinetic energy from particles (atoms or molecules) with greater kinetic energy to those with lower kinetic energy. In this respect, the process can be viewed in terms of collisions, as described through classical mechanics. Consider the particles in two substances at different temperatures. The particles of each substance move with a range of speeds that are distributed around a mean value, $\overline{v}$ . The temperature of each substance is defined in terms of the average kinetic energy of its particles, $\frac{1}{2}m{\overline{v}}^2$ . The simplest mathematical description of this is for an ideal gas, and is given by the following equation:

where k is Boltzmann’s constant ( $k=1.38\times {\text{10}}^{-\text{23}}\text{ J/K}$ ). The equations for non-ideal gases, liquids, and solids are more complicated, but the general relation between the kinetic energies of the particles and the overall temperature of the substance still holds: the particles in the substance with the higher temperature have greater average kinetic energies than do the particles of a substance with a lower temperature.

When the two substances are in thermal contact, the particles of both substances can collide with each other. In the vast majority of collisions, a particle with greater kinetic energy will transfer some of its energy to a particle with lower kinetic energy. By giving up this energy, the average kinetic energy of this particle is reduced, and therefore, the temperature of the substance associated with that particle decreases slightly. Similarly, the average kinetic energy of the particle in the second substance increases through the collision, causing that substance’s temperature to increase by a minuscule amount. In this way, through a vast number of particle collisions, thermal energy is transferred macroscopically from the substance with greater temperature (that is, greater internal energy) to the substance with lower temperature (lower internal energy).

Macroscopically, heat appears to transfer thermal energy spontaneously in only one direction. When interpreted at the microscopic level, the transfer of kinetic energy between particles occurs in both directions. This is because some of the particles in the low-temperature substance have higher kinetic energies than the particles in the high-temperature substance, so that some of the energy transfer is in the direction from the lower temperature substance to the higher temperature substance. However, much more of the energy is transferred in the other direction. When thermal equilibrium is reached, the energy transfer in either direction is, on average, the same, so that there is no further change in the internal energy, or temperature, of either substance.