Consider a gas of “hard spheres,” which do not interact at

Chapter 8, Problem 11P

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QUESTION:

Consider a gas of “hard spheres,” which do not interact at all unless their separation distance is less than \(r_{0}\), in which case then interaction energy is infinite. Sketch the Mayer \(f\)-function for this gas, and compute the second virial coefficient. Discuss the result briefly.

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QUESTION:

Consider a gas of “hard spheres,” which do not interact at all unless their separation distance is less than \(r_{0}\), in which case then interaction energy is infinite. Sketch the Mayer \(f\)-function for this gas, and compute the second virial coefficient. Discuss the result briefly.

ANSWER:

Step 1 of 4

The mathematical equation for Mayer’s function is given by,

\(f(r)=e^{-\beta u(r)}-1\)

Here the factor

\(\beta=\frac{1}{k T_{c}}\)    

Here \(T_{c}\) is the critical temperature and \(k\) is the Boltzmann constant.

The Mayer’s expression is written as,

\(f(r)=e^{-\frac{u(r)}{k T}-1}\)

Here \(u(r)\) is the potential energy due to interaction of any pair of molecules.

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