Let's analyze what happens to the temperatures of melting ice and boiling water given the conditions in the laboratory.
### Melting Ice at [tex]\(0^\circ C\)[/tex]
1. Phase Change of Ice to Water:
- When ice melts, it remains at [tex]\(0^\circ C\)[/tex] until all of the ice has transitioned to liquid water.
2. Thermodynamics:
- For ice to melt into water, it needs to absorb heat from the surroundings. However, during this phase change, the temperature of the ice-water mixture does not increase.
3. Constant Temperature:
- Therefore, the temperature of the melting ice remains constant at [tex]\(0^\circ C\)[/tex].
### Boiling Water at [tex]\(100^\circ C\)[/tex]
1. Phase Change of Water to Steam:
- When water boils, it is undergoing a phase change from liquid to steam at [tex]\(100^\circ C\)[/tex].
2. Heat Absorption and Boiling Point:
- Similar to the melting process, boiling water will absorb heat without a change in temperature because the energy is used to convert water into steam.
3. Constant Temperature:
- Thus, as long as the water is boiling, the temperature will remain constant at [tex]\(100^\circ C\)[/tex].
### Conclusion
Given these explanations, both the temperature of the melting ice and the temperature of the boiling water remain constant under the specified conditions.
Therefore, the correct answer is:
[tex]\[
\begin{array}{|c|c|c|}
\hline & \text{temperature of} \\
\text{melting ice}
& \text{temperature of} \\
\text{boiling water}
\\
\hline A & \text{constant} & \text{constant} \\
\hline
\end{array}
\][/tex]
