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The specific heat capacity of a substance, usually denoted by or , is the heat capacity of a sample of the substance, divided by the mass of the sample: [10] = =, where represents the amount of heat needed to uniformly raise the temperature of the sample by a small increment .
Systems do not contain work, but can perform work, and likewise, in formal thermodynamics, systems do not contain heat, but can transfer heat. Informally, however, a difference in the energy of a system that occurs solely because of a difference in its temperature is commonly called heat , and the energy that flows across a boundary as a result ...
T is the temperature in particular case of heat transfer otherwise it is the variable of interest; t is time; c is the specific heat; u is velocity; ε is porosity that is the ratio of liquid volume to the total volume; ρ is mass density; λ is thermal conductivity; Q(x,t) is source term representing the capacity of internal sources
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.
where is the specific heat capacity (at constant pressure, in case of a gas) and is the density (mass per unit volume) of the material. This derivation assumes that the material has constant mass density and heat capacity through space as well as time.
Also for substances that are nearly incompressible, such as solids and liquids, the difference between the two specific heats is negligible. As the absolute temperature of the system approaches zero, since both heat capacities must generally approach zero in accordance with the Third Law of Thermodynamics , the difference between C P ,m and C V ...
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The contribution of the muscle to the specific heat of the body is approximately 47%, and the contribution of the fat and skin is approximately 24%. The specific heat of tissues range from ~0.7 kJ · kg−1 · °C−1 for tooth (enamel) to 4.2 kJ · kg−1 · °C−1 for eye (sclera).