Question

Two identical pans sit on a stove. Pan A contains a mixture of water and ice. Pan B contains an equal volume of water that is chilled to the same temperature. How will the temperatures of the contents change as the pans are heated? Each pan contains a thermometer that records the temperature of the water and of the water-ice mixture. The stove is turned to high, and both pans are heated until boiling occurs. Heat continues to be applied for several more minutes. Plot separate curves on the following graph to illustrate how temperature changes with time for both pans throughout the experiment. Label the curves.

Short answer

Pan A stays at 0°C until ice melts; both pans then heat to 100°C and boil.

Step-by-step solution

Understand the Initial Conditions

Both pans start at the same initial temperature below the freezing point. Pan A has both water and ice, while Pan B has only water that is chilled to the same initial temperature.

Pan A Temperature Analysis

As heat is applied, the temperature of the water-ice mixture in Pan A will remain constant at 0°C until all the ice melts. This phase change involves latent heat absorption, keeping the temperature steady.

Pan B Temperature Analysis

In Pan B, the temperature will rise steadily as it absorbs heat, since there is only liquid water. This continues until the water reaches 100°C.

After Ice Melts in Pan A

Once all the ice in Pan A is melted, the temperature of the now all-liquid water will begin to rise linearly until it reaches 100°C, similar to Pan B.

Both Pans Reach Boiling Point

Both Pan A and Pan B will have their temperatures plateau at 100°C as water begins to boil. This temperature will remain constant despite continued heat application, due to the latent heat of vaporization.

Graphing the Temperature Curves

On the graph, for Pan A, plot a constant 0°C line until all the ice melts, then a linear rise to 100°C. For Pan B, draw a steadily rising line from the initial temperature until it reaches 100°C. Both lines should flatten at 100°C due to boiling.

Key concepts

Phase Change

A phase change is a transformation from one state of matter to another. This experiment demonstrates phase change in Pan A when ice transitions to water. It starts with both ice and liquid water present in Pan A. As heat is applied, the temperature doesn't rise until all the ice melts, even though heat is continuously added. This is because energy is used for the phase change. Phase transitions include:

• Melting: Solid to liquid
• Freezing: Liquid to solid
• Boiling/Evaporation: Liquid to gas

During phase changes, temperatures remain constant, as seen in Pan A when ice melts.

Latent Heat

Latent heat refers to the energy absorbed or released during a phase change without temperature change. In Pan A, the latent heat of fusion is what maintains the constant temperature as the ice absorbs energy to melt. After the ice has fully melted, any additional heat leads to a temperature increase in the now liquid water. Similarly, when water reaches its boiling point, the latent heat of vaporization comes into play. At this temperature, energy is used to turn liquid water into vapor instead of increasing temperature. Key points:

• Measure of energy for phase change
• No temperature change during absorption/release
• Important in melting and boiling processes

Temperature Curves

Temperature curves help visualize how temperature changes over time. In our scenario, plotting these curves for Pan A and Pan B provides an insight into the heating process. For Pan A, the curve remains flat at 0°C while ice melts, then rises until 100°C. For Pan B, the curve steadily rises from the initial temperature to 100°C. Once boiling begins, both curves level off, showing that the temperature remains constant despite continued heating. This illustration can be used to understand thermal dynamics better. Features of the curves:

• Flat segments indicate phase changes
• Rising segments indicate temperature increase
• Steady segments at boiling point

Boiling Point

The boiling point is the temperature where a liquid becomes gas. For water at sea level, this is 100°C. In both pans, once the temperature reaches this point, it doesn't rise further despite ongoing heat, as energy is used for converting the liquid to gas. This experiment demonstrates how boiling points are crucial when considering energy allocation in heating processes. Both Pan A and Pan B stop rising at the boiling point, providing an excellent example of energy utilization during a phase transition.

Thermal Equilibrium

Thermal equilibrium refers to a state in which all parts of a system are at the same temperature and no heat flows between them. In our experiment, this concept appears multiple times as the system reaches various equilibria. Initially, Pan B's water reaches thermal equilibrium quickly as it begins to heat uniformly. In contrast, Pan A only achieves equilibrium after all ice melts and the mixture eventually heats up. Final equilibrium is achieved in both pans when they reach their boiling points, where the temperature stops rising despite continuous heat input. This occurs due to the continued phase change from liquid to gas. Thermal equilibrium is crucial for stability in thermal systems.