# Thermal Mass - Background

Background

The equation relating thermal energy to thermal mass is:

where Q is the thermal energy transferred, Cth is the thermal mass of the body, and ΔT is the change in temperature.

For example, if 250 J of heat energy is added to a copper gear with a thermal mass of 38.46 J/°C, its temperature will rise by 6.50 °C. If the body consists of a homogeneous material with sufficiently known physical properties, the thermal mass is simply the mass of material present times the specific heat capacity of that material. For bodies made of many materials, the sum of heat capacities for their pure components may be used in the calculation, or in some cases (as for a whole animal, for example) the number may simply be measured for the entire body in question, directly.

As an extensive property, heat capacity is characteristic of an object; its corresponding intensive property is specific heat capacity, expressed in terms of a measure of the amount of material such as mass or number of moles, which must be multiplied by similar units to give the heat capacity of the entire body of material. Thus the heat capacity can be equivalently calculated as the product of the mass m of the body and the specific heat capacity c for the material, or the product of the number of moles of molecules present n and the molar specific heat capacity . For discussion of why the thermal energy storage abilities of pure substances vary, see factors that affect specific heat capacity.

For a body of uniform composition, can be approximated by

where is the mass of the body and is the isobaric specific heat capacity of the material averaged over temperature range in question. For bodies composed of numerous different materials, the thermal masses for the different components can just be added together.

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