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

Chapter 8, Problem 11P

(choose chapter or problem)

Get Unlimited Answers! Check out our subscriptions
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.

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.

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.