Thermal reservoir

A thermal reservoir, also thermal energy reservoir or thermal bath, is a thermodynamic system with a heat capacity so large that the temperature of the reservoir changes relatively little when a significant amount of heat is added or extracted.^[1] As a conceptual simplification, it effectively functions as an infinite pool of thermal energy at a given, constant temperature. Since it can act as an inertial source and sink of heat, it is often also referred to as a heat reservoir or heat bath.^[2]

Lakes, oceans and rivers often serve as thermal reservoirs in geophysical processes, such as the weather. In atmospheric science, large air masses in the atmosphere often function as thermal reservoirs.^[3]

Since the temperature of a thermal reservoir T does not change during the heat transfer, the change of entropy in the reservoir is: $${\displaystyle dS_{\text{Res}}={\frac {\delta Q}{T}}}$$ where ${\displaystyle \delta Q}$ is the incremental reversible transfer of heat energy into the reservoir.

The microcanonical partition sum ${\displaystyle Z(E)}$ of a heat bath of temperature T has the property: $${\displaystyle Z(E+\Delta E)=Z(E)e^{\Delta E/k_{\text{B}}T}}$$ where ${\displaystyle k_{\text{B}}}$ is the Boltzmann constant. It thus changes by the same factor when a given amount of energy is added. The exponential factor in this expression can be identified with the reciprocal of the Boltzmann factor.^[4]

For an engineering application, see geothermal heat pump.