3. (Gaskell 7.8) Nitrogen has a triple point at \( P=4650 \mathrm{~atm} \) and \( T=44.5 \mathrm{~K} \), at which state the allotropes \( \alpha, \beta \) and \( \gamma \) coexist in equilibrium with one another. At the triple point, \( V_{\theta}-V_{\alpha}= \) \( 0.043 \mathrm{~cm}^{3} / \mathrm{mole} \) and \( V_{\alpha}-V_{\gamma}=0.165 \mathrm{~cm}^{3} / \mathrm{mole} \). Also at the triple point, \( s_{B}-S_{\alpha}=4.59 \mathrm{~J} / \mathrm{K} \) and \( S_{a}-S_{Y}=1.25 \mathrm{~J} / \mathrm{K} \). The state \( P=1 \mathrm{~atm} \) and \( T=36 \mathrm{~K} \) lies on the boundary between the fields of stability of the \( \alpha \) and \( \beta \) phases, and at this state, for the transformation \( \alpha \rightarrow \beta, \Delta S=6.52 \mathrm{I} / \mathrm{K} \) and \( \Delta V=0.22 \mathrm{~cm}^{3} / \mathrm{mole} \). Sketch (to the best your ability with the help of some software, e.g., Excel) the phase diagram ( \( P \) V \( \mathrm{rs} . T) \) for nitrogen at low temperature.