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Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
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:
The ideal gas law is the equation of state for an ideal gas, given by: = where P is the pressure; V is the volume; n is the amount of substance of the gas (in moles) T is the absolute temperature; R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature.
For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.
The heat content of an ideal gas is independent of pressure (or volume), but the heat content of real gases varies with pressure, hence the need to define the state for the gas (real or ideal) and the pressure. Note that for some thermodynamic databases such as for steam, the reference temperature is 273.15 K (0 °C).
The laws describing the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions are called gas laws.The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
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
The ideal gas law can be recast into the formula: p ρ = T m {\displaystyle {\frac {p}{\rho }}={\frac {T}{m}}} By substituting this ratio in the Newton–Laplace law, the expression of the sound speed into an ideal gas as function of temperature is finally achieved.