What does a point on a phase boundary in a \(p\)-\(T\) phase diagram represent?

What is the triple point of a substance?

Below the triple-point pressure, a solid is heated. What phase change can occur instead of melting?

A substance is above its critical temperature. Can a sharp liquid-gas phase boundary be crossed by changing pressure alone? Explain.

For a vaporization boundary, \(L>0\) and the gas specific volume is larger than the liquid specific volume. Use the Clapeyron relation to determine the sign of \(dp/dT\).

On a phase diagram, explain the difference between being inside a phase region and being on a phase boundary.

For a transition with \(L=2.5\times10^5\,\mathrm{J\,kg^{-1}}\), \(T=400\,\mathrm{K}\), and \(\Delta v=0.80\,\mathrm{m^3\,kg^{-1}}\), estimate the phase-boundary slope \(dp/dT\).

Water's solid-liquid boundary has a negative slope. Using the Clapeyron relation and \(L>0\), what does this imply about \(\Delta v=v_{\mathrm{liquid}}-v_{\mathrm{solid}}\) for melting?

A sealed sample contains liquid and vapor in equilibrium. The volume is slowly reduced at constant temperature below the critical temperature. Explain why pressure can remain nearly constant while the relative amounts of liquid and vapor change.

Starting from \(dp/dT=L/(T\Delta v)\), derive the approximate Clausius-Clapeyron form \(d\ln p/dT=L/(RT^2)\) for vaporization by assuming the vapor is ideal and the liquid volume is negligible.

A phase boundary has slope \(dp/dT=2.0\times10^5\,\mathrm{Pa\,K^{-1}}\) at \(T=300\,\mathrm{K}\). If the specific-volume change is \(\Delta v=1.2\times10^{-3}\,\mathrm{m^3\,kg^{-1}}\), estimate the latent heat per kilogram using the Clapeyron relation.

A substance has a vaporization latent heat \(L=3.0\times10^5\,\mathrm{J\,kg^{-1}}\), temperature \(350\,\mathrm K\), and \(\Delta v=0.50\,\mathrm{m^3\,kg^{-1}}\). Find \(dp/dT\).

Explain why boiling temperature changes with external pressure.

Why does adding heat during a phase change not necessarily raise temperature?

A sample is at its triple point. What happens if temperature is held fixed but pressure is changed slightly?

Derive the sign of the solid-liquid boundary slope for a substance whose liquid is denser than its solid.

Derive the integrated Clausius-Clapeyron form \(\ln(p_2/p_1)=-(L/R)(1/T_2-1/T_1)\) for constant molar latent heat.

Explain why there is no sharp distinction between liquid and gas above the critical point.

Use a phase diagram to explain why carbon dioxide can sublime at atmospheric pressure.

Connect latent heat, phase coexistence, and the Clapeyron relation in one explanation.