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The reduced temperature of a fluid is its actual temperature, divided by its critical temperature: [1] = where the actual temperature and critical temperature are expressed in absolute temperature scales (either Kelvin or Rankine). Both the reduced temperature and the reduced pressure are often used in thermodynamical formulas like the Peng ...
Once two of the three reduced properties are found, the compressibility chart can be used. In a compressibility chart, reduced pressure is on the x-axis and Z is on the y-axis. When given the reduced pressure and temperature, find the given pressure on the x-axis. From there, move up on the chart until the given reduced temperature is found.
According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. [1] [2]
The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The deviation is −1.63 kPa or −1.61 %. It is important to use the same absolute units for T and T c as well as for P and P c. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values T r and P r.
In other words, the same equation relates the reduced volume, reduced pressure, and reduced temperature for all substances. Obviously such a broad general relation is unlikely to be correct; nevertheless, the fact that one can obtain from it an essentially correct description of actual phenomena is very remarkable.
Out of the total pressure in Eq.(1), the first term pressures on the right side of Ag, Cu, Mo, Pd at room temperature are consistent in a wide pressure range, according to the Mao ruby scale up to 1 Mba. [5] In addition, the first term pressure of Ag, Cu, and MgO are consistent according to third-order Birch–Murnaghan equation of state. [6]
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
Figure 1: Thermal pressure as a function of temperature normalized to A of the few compounds commonly used in the study of Geophysics. [3]The thermal pressure coefficient can be considered as a fundamental property; it is closely related to various properties such as internal pressure, sonic velocity, the entropy of melting, isothermal compressibility, isobaric expansibility, phase transition ...