Question

Sketch a qualitatively accurate graph of the entropy of a substance (perhaps${\mathrm{H}}_2\mathrm{O}$ ) as a function of temperature, at fixed pressure. Indicate where the substance is solid, liquid, and gas. Explain each feature of the graph briefly.

Short answer

The graph of the entropy of a substance as a function of temperature, at fixed pressure can be sketched as below:

Step-by-step solution

Given Information

A graph of a substance is to be made showing the entropy of a substance as a function of temperature.

It is also given that the pressure should be constant.

Explanation

It is given that the pressure should be fixed.

Hence, the entropy at constant pressure is given as:

$$\begin{gathered} dS=\frac{C_{p}dT}{T} \\ {\left(\frac{dS}{dT}\right)}_P=\frac{C_p}{T} \end{gathered}$$

The graph can be sketched as below:

From the graph, it can be seen that at low temperatures, the slope of the solid is zero. As the temperature rises, so does the slope, causing the solid to melt. At the same temperature, this increases entropy. The curve grows shallower as the solid melts, showing the liquid-gas phase.

Final answer

The required graph can be sketched as below: