Step 1: Analyzing the phase diagram.
The phase diagram presented shows the stability fields for minerals P and Q with respect to pressure and temperature. The boundaries between the stability fields indicate the conditions under which these minerals can coexist, and the liquid phase is shown as a distinct region.
Step 2: Understanding the coexistence of P and Q.
- Option (A): P and Q can coexist at different temperatures only if pressures are different. This is correct. The phase diagram shows that P and Q can coexist at different temperatures, but they require different pressure conditions to do so.
- Option (B): P and Q can coexist with liquid only at one pressure and temperature. This is incorrect. The diagram shows that P and Q can coexist with the liquid phase at more than one combination of pressure and temperature, meaning they can coexist under varying conditions, not just one specific pair of values.
- Option (C): Q has a higher melting temperature at higher pressures than at lower pressures. This is correct. The phase diagram suggests that the melting temperature of Q increases with pressure.
- Option (D): A reaction forming Q from P at constant pressure will require an input of heat. This is correct. The phase diagram suggests that forming Q from P at constant pressure requires an increase in temperature (input of heat).
Step 3: Conclusion.
The incorrect statement is (B), as the diagram shows that P and Q can coexist with liquid at different pressures and temperatures, not just at one specific condition.
\[
\boxed{\text{P and Q can coexist with liquid only at one pressure and temperature}}
\]