- #1

Diracobama2181

- 75

- 2

- Homework Statement
- Numerically evaluate the second viral coefficient of the Lennard-Jones Potential. The result should be expressed in the form of a dimensional constant times

a dimensionless function of the dimensionless variable $$ E_0 \beta$$

- Relevant Equations
- $$U=E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)$$

$$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$

I get

$$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$

as the coefficient. I was just unsure how to evaluate it numerically from here. Any suggestions would be appreciated. Thank you.

$$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$

as the coefficient. I was just unsure how to evaluate it numerically from here. Any suggestions would be appreciated. Thank you.