Thermal Energy Flow

If two identical bodies at different temperatures are in contact, thermal energy will always flow from one to the other in such a direction as to increase the total entropy. In which direction will this flow be? That depends on two factors, the amount of energy and entropy the two bodies already contain. The second law of thermodynamics implies that thermal energy must flow toward the region of lower temperature that is, each unit of thermal energy acquires greater disorder as it moves into the cooler region. Why?

Answer

The classical flow of thermal energy toward the cooler region occurs because the free energy of the combined system E_free = E_sys – TS becomes less, where T is the temperature and S is the entropy. If the free energy is the same at two temperatures, one can see that for a given amount of system energy there is more disorder at the lower temperature. Assuming that the two-block system initially simply transfers thermal energy from the warmer to the cooler block, with no other energy transfers, then a cooler system is preferred.