Equation of state for ideal gases

Equation of State for Ideal Gases mathematical statement relating conditions of pressure, volume, absolute temperature, and amount of substance PV = nRT... 

The specific energy of an explosive is defined as its working performance per kg, calculated theoretically from the equation of state for ideal gases ... 

Let us assume that two containers, each containing a different gas are linked by a thin pipe between them, Fig. 1.44. Equimolar counter diffusion will also take place in this case, if the pressure and temperature of both the gases are the same and obey the thermal equation of state for ideal gases. 

As an example we will take a porous body into which hydrogen diffuses. A volume element in the porous body has a certain mass and therefore a certain density, e.g. p = 7.8 103 kg/m3. According to this a volume element of 1 mm3 has a mass of 7.8 10-3 g. We assume that the volume element is at the ambient temperature 298 K with a partial pressure of hydrogen of p = 1 hPa. The equation of state for ideal gases is used to find the hydrogen absorbed by the volume element, which is... 

The loss of hydrogen follows from the equation of state for ideal gases... 

Equation of State for Ideal Gases at Very Low Temperatures.—If, as we have done throughout, we denote the negative energy content of the system by U, the formulae of the previous section show that at the absolute zero... 

When new legislation was introduced exempting science students from a classical education, van der Waals was finally allowed to sit for his university examinations. In 1873 he obtained his doctorate with a thesis titled, On the Continuity of the Gas and Liquid State. His thesis proposed a correction to the equation of state for ideal gases that would allow the equation to be applied to real gases. That is, he proposed a modification of the formula PV = nRT to account for the fact that atoms are real and that they interact. 

In order to use the laws of ideal gas for real solutions, Lewis in 1901 introduced a notion of fugacity (volatility). He proposed not to change equations of state for ideal gases but only to modify the values of partial pressures in them. Fugacity of a component i is its modified partial pressure, which under real conditions does not contradict equations of state of the ideal gas. Fugacity in its substance is partial pressure, which accoxmts for the effect of the forces of intermolecular interaction and is measured in units of pressure. 

In the case of real gases, departure from the theoretical equation of state for ideal gases can be expressed in different ways that have led historically to various equations of state among which the Van der Waals and the virial equations are the most noticeable. Other more complex equations of state for real gases are also briefly mentioned. 

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