# How to prove it mathematically that either rhombic or the monoclinic sulfur is denser?

For the transition, rhombic sulfur → monoclinic sulfur, the value of $$ΔS$$ is positive. The transition temperature increases with increase in pressure. Which is denser, the rhombic or the monoclinic form? Prove your answer mathematically.

I tried by using Clapeyron equation but still failed. How should I approach and solve it? This is so tricky.

$$\frac{\mathrm dP}{\mathrm dT} = \frac{\Delta_\mathrm{trs}S}{\Delta_\mathrm{trs}V}$$
$$\Delta_\mathrm{trs}S$$ is positive. $$\displaystyle\frac{\mathrm dP}{\mathrm dT}$$ is said to be positive as well. Thus, $$\Delta_\mathrm{trs}V$$ has to be positive, i.e. monoclinic sulfur has a greater molar volume, and thus rhombic sulfur is denser.