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Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about 4184 J⋅kg −1 ⋅K −1 at 20 °C; but that of ice, just below 0 °C, is only 2093 J⋅kg −1 ⋅K −1.
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
This relation was built on the reasoning that energy must be supplied to raise the temperature of the gas and for the gas to do work in a volume changing case. According to this relation, the difference between the specific heat capacities is the same as the universal gas constant. This relation is represented by the difference between Cp and Cv:
In the anisotropic case where the coefficient matrix A is not scalar and/or if it depends on x, then an explicit formula for the solution of the heat equation can seldom be written down, though it is usually possible to consider the associated abstract Cauchy problem and show that it is a well-posed problem and/or to show some qualitative ...
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.
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). [13]
The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity.
An additional factor for all types of specific heat capacities (including molar specific heats) then further reflects degrees of freedom available to the atoms composing the substance, at various temperatures. For most liquids, the volumetric heat capacity is narrower, for example octane at 1.64 MJ⋅K −1 ⋅m −3 or ethanol at 1.9. This ...