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The steady-state heat equation for a volume that contains a heat source (the inhomogeneous case), is the Poisson's equation: − k ∇ 2 u = q {\displaystyle -k\nabla ^{2}u=q} where u is the temperature , k is the thermal conductivity and q is the rate of heat generation per unit volume.
(Note - the relation between pressure, volume, temperature, and particle number which is commonly called "the equation of state" is just one of many possible equations of state.) If we know all k+2 of the above equations of state, we may reconstitute the fundamental equation and recover all thermodynamic properties of the system.
Therefore, gas volume may alternatively be expressed excluding the humidity content: V d (volume dry). This fraction more accurately follows the ideal gas law. On the contrary, V s (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity).
The mathematical equation for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process can be represented by the polytropic process equation [3] =, where P is pressure, V is volume, and γ is the adiabatic index or heat capacity ratio defined as
The state of an amount of gas is determined by its pressure, volume, and temperature. The modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature: the appropriate SI unit is the kelvin. [4]
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:
where V 100 is the volume occupied by a given sample of gas at 100 °C; V 0 is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so is not what became known as Charles's Law.
An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict ...