Some researchers at the Modford Institute of Taxidermy claim...

Some researchers at the Modford Institute of Taxidermy claim to have measured the following pressure-temperature phase diagram of a new substance, which they call "embalmium". Their results show that along the phase lines near the triple point $$ 0<\left(\frac{d p}{d T}\right)_{\text {sublimation }}<\left(-\frac{d p}{d T}\right)_{\text {fusion }}<\left(\frac{d p}{d T}\right)_{\text {vaporization }} $$ as indicated in the diagram. If these results are correct, "embalmium" has one rather unusual property and one property which violates the laws of thermodynamics. What are the two properties? FIGURE CAN'T COPY.

Some researchers at the Modford Institute of Taxidermy claim to have measured the following pressure-temperature phase diagram of a new substance, which they call "embalmium". Their results show that along the phase lines near the triple point
$$
0<\left(\frac{d p}{d T}\right)_{\text {sublimation }}<\left(-\frac{d p}{d T}\right)_{\text {fusion }}<\left(\frac{d p}{d T}\right)_{\text {vaporization }}
$$
as indicated in the diagram. If these results are correct, "embalmium" has one rather unusual property and one property which violates the laws of thermodynamics. What are the two properties?
FIGURE CAN'T COPY.

Key Concepts

Pressure–Temperature Phase Diagrams

A pressure–temperature phase diagram displays the conditions of pressure and temperature under which a substance exists in different phases (solid, liquid, gas) and shows the boundaries (phase lines) where phase transitions occur. These diagrams are essential for understanding the equilibrium between phases and how changes in external conditions lead to transitions.

Phase Transitions

Phase transitions refer to the transformation between different states of matter – such as sublimation (solid to gas), fusion (solid to liquid), and vaporization (liquid to gas). Each transition involves an exchange of energy (latent heat) and characteristic changes in volume, which determine the slopes of the phase boundaries indicated in phase diagrams.

Triple Point

The triple point is the unique set of pressure and temperature conditions at which three phases of a substance coexist in equilibrium. It is a critical concept in thermodynamics because it provides a fixed reference point and the behavior of phase transition slopes near this point can reveal subtle properties of the substance.

Clapeyron Equation

The Clapeyron equation provides a quantitative relationship between the slope of a phase boundary in a pressure–temperature diagram, the latent heat of the phase transition, and the change in volume during the transition. It is used to predict how the equilibrium conditions shift with changes in pressure or temperature and to compare the energetics of different phase changes.

Density Anomaly

A density anomaly occurs when the density ordering of phases is unusual compared with most substances. For example, if the melting (fusion) curve of a substance has a negative slope, it implies that the liquid phase is denser than the solid phase—a characteristic observed in water. In the context of the question, such an unusual slope indicates an anomalous density relationship between the solid and liquid phases.

Thermodynamic Consistency

Thermodynamic consistency involves ensuring that the experimental or derived values for latent heats and phase boundary slopes obey fundamental thermodynamic laws. In this case, the measured ordering of slopes near the triple point implies, via the Clapeyron equation, that the latent heat of fusion is anomalously high—potentially even rivaling that of vaporization—which violates the expected energy considerations where melting requires far less energy than vaporization.

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