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In those contexts, the unit of heat capacity is 1 BTU/°R ≈ 1900 J/K. [5] The BTU was in fact defined so that the average heat capacity of one pound of water would be 1 BTU/°F. In this regard, with respect to mass, note conversion of 1 Btu/lb⋅°R ≈ 4,187 J/kg⋅K [ 6 ] and the calorie (below).
For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg −1 ⋅K −1. [ 3 ] Specific heat capacity often varies with temperature, and is different for each state of matter .
Data in the table above is given for water–steam equilibria at various temperatures over the entire temperature range at which liquid water can exist. Pressure of the equilibrium is given in the second column in kPa. The third column is the heat content of each gram of the liquid phase relative to water at 0 °C.
The heat capacity depends on how the external variables of the system are changed when the heat is supplied. If the only external variable of the system is the volume, then we can write: d S = ( ∂ S ∂ T ) V d T + ( ∂ S ∂ V ) T d V {\displaystyle dS=\left({\frac {\partial S}{\partial T}}\right)_{V}dT+\left({\frac {\partial S}{\partial V ...
The Black–Scholes equation of financial mathematics is a small variant of the heat equation, and the Schrödinger equation of quantum mechanics can be regarded as a heat equation in imaginary time. In image analysis , the heat equation is sometimes used to resolve pixelation and to identify edges .
In general, the energy eigenstates of the system will depend on x. According to the adiabatic theorem of quantum mechanics, in the limit of an infinitely slow change of the system's Hamiltonian, the system will stay in the same energy eigenstate and thus change its energy according to the change in energy of the energy eigenstate it is in.
The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so the term 'heat flow' is a redundancy (i.e. a pleonasm ).
Heat conduction in a Newtonian context is modelled by the Fourier equation, [4] namely a parabolic partial differential equation of the kind: = , where θ is temperature, [5] t is time, α = k/(ρ c) is thermal diffusivity, k is thermal conductivity, ρ is density, and c is specific heat capacity.