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In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the ...
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
where Q is the thermal energy transferred, C th 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.
Thus, they are essentially equations of state, and using the fundamental equations, experimental data can be used to determine sought-after quantities like G (Gibbs free energy) or H . [1] The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy , and volume for a closed system in ...
Only one equation of state will not be sufficient to reconstitute the fundamental equation. All equations of state will be needed to fully characterize the thermodynamic system. Note that what is commonly called "the equation of state" is just the "mechanical" equation of state involving the Helmholtz potential and the volume:
The author then explains how heat is defined or measured by calorimetry, in terms of heat capacity, specific heat capacity, molar heat capacity, and temperature. [ 42 ] A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined ...
The heat capacity of an object is an amount of energy divided by a temperature change, which has the dimension L 2 ⋅M⋅T −2 ⋅Θ −1. Therefore, the SI unit J/K is equivalent to kilogram meter squared per second squared per kelvin (kg⋅m 2 ⋅s −2 ⋅K −1 ).
If its temperature is allowed to change by 1 °C, its mass changes by 1.5 picograms (1 pg = 1 × 10 −12 g). [note 5] A spinning ball has greater mass than when it is not spinning. Its increase of mass is exactly the equivalent of the mass of energy of rotation, which is itself the sum of the kinetic energies of all the moving parts of the ball.