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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.
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 P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
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:
In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
In thermodynamics, Bridgman's thermodynamic equations are a basic set of thermodynamic equations, derived using a method of generating multiple thermodynamic identities involving a number of thermodynamic quantities. The equations are named after the American physicist Percy Williams Bridgman.
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The zeroth law of thermodynamics states: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other. This statement implies that thermal equilibrium is an equivalence relation on the set of thermodynamic systems under consideration.