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what are virial coefficients

what are virial coefficients

Grade:12

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Avinash
askIITians Faculty 1241 Points
8 years ago
The virial expansion, also called the virial equation of state, is the most interesting and versatile of the equations of state for gases.. The virial expansion is a power series in powers of the variable,n/V,and has the form,

(1)check image .

The coefficient,B(T), is a function of temperature and is called the "second virial coefficient.C(T) is called the third virial coefficient, and so on. The expansion is, in principle, an infinite series, and as such should be valid for all isotropic substances. In practice, however, terms above the third virial coefficient are rarely used in chemical thermodynamics.

Notice that we have set the quantitypV/nRTequal toZ. This quantity (Z) is called the "compression factor." It is a useful measure of the deviation of a real gas from an ideal gas. For an ideal gas the compression factor is equal to 1.

The Boyle Temperature

The second virial coefficient,B(T), is an increasing function of temperature throughout most of the useful temperature range. (It does decrease slightly at very high temperatures.)Bis negative at low temperatures, passes through zero at the so-called "Boyle temperature," and then becomes positive. The temperature at whichB(T) = 0is called the Boyle temperature because the gas obeys Boyle's law to high accuracy at this temperature. We can see this by noting that at the Boyle temperature the virial expansion looks like, .

If the density is not too high theCterm is very small so that the system obeys Boyle's law.

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