Consider a classical system of noninteracting, diatomic molecules enclosed in a box of volume \(V\) at temperature \(T\). The Hamiltonian of a single molecule is given by

\[
H\left(\boldsymbol{r}_{1}, \boldsymbol{r}_{2}, \boldsymbol{p}_{1}, \boldsymbol{p}_{2}ight)=\frac{1}{2 m}\left(p_{1}^{2}+p_{2}^{2}ight)+\frac{1}{2} K\left|\boldsymbol{r}_{1}-\boldsymbol{r}_{2}ight|^{2} .
\]

Study the thermodynamics of this system, including the dependence of the quantity \(\left\langle r_{12}^{2}ightangle\) on \(T\).