Problem 52 - University Physics with Modern Physics

Question

A physicist places a piece of ice at \(0.00^{\circ} \mathrm{C}\) and a beaker of water at \(0.00^{\circ} \mathrm{C}\) inside a glass box and closes the lid of the box. All the air is then removed from the box. If the ice, water, and beaker are all maintained at a temperature of \(0.00^{\circ} \mathrm{C},\) describe the final equilibrium state inside the box.

Step-by-Step Solution

Answer

At equilibrium, ice and water coexist at 0.00°C with no net melting or freezing due to the vacuum.

Step 1: Understand the Initial Conditions

The initial condition is that both the ice and water are at the melting point, which is exactly 0.00°C. This is the temperature where ice can coexist with water without any heat exchange. All air has been evacuated from the box, meaning the system is in a vacuum.

Step 2: Analyze the Thermal Dynamics

Since the temperature is maintained at 0.00°C and there is no air in the box to facilitate heat exchange, no further phase change can occur. The ice won't melt into water because additional energy (from heat) is required to transition from solid to liquid.

Step 3: Consider the Phase Equilibrium

At 0.00°C in a vacuum, the system will reach an equilibrium where ice and water coexist. There is no net change in the amount of ice or water as the system is closed, and no heat can be transferred in or out of the system.

Step 4: Conclude the Equilibrium State

The final equilibrium state within the box is one where there is both ice and water present, as no melting or freezing occurs in the absence of an external energy source. This is due to the lack of heat movement at 0.00°C in this vacuum-sealed environment.

Key Concepts

Melting Point

The melting point of a substance is the temperature at which the solid form of the substance turns into its liquid form. For water, the melting point is precisely 0.00°C. This point is significant because both phases, solid (ice) and liquid (water), can exist together in equilibrium at this temperature. In this exercise, the ice and water are at their melting point, indicating that no additional heat is being added or removed from the system, and thus, no phase change is expected to occur.

At the melting point, if any heat were added to the system, it would start converting some of the ice into water. Conversely, removing heat would turn some of the water into ice. However, since the exercise specifies maintaining a constant 0.00°C, no such changes happen. The melting point is a key part of determining the equilibrium state within the system.

Thermal Dynamics

Thermal dynamics involves the study of energy transfer in the form of heat. In an isolated system such as the one described in this exercise, the thermal dynamics are quite straightforward. When the ice and water are both at 0.00°C, they are at thermal equilibrium, meaning their temperatures are equal, and thermal energy (heat) isn't moving between them.

One of the important aspects of thermal dynamics is the idea of thermal insulation, which is effectively provided by a vacuum. Without the presence of air in the box, there is no medium for heat to conduct through, which keeps the system isolated from any external thermal interactions.

• There is no additional energy added to the system.
• The thermal equilibrium means no phase change occurs without an energy source.

In thermal dynamics, the system remains in a stable state as long as the conditions don't change, reinforcing the idea that ice and water will stay as they are in this scenario.

Vacuum System

A vacuum system refers to an environment from which air and any other matter are nearly completely removed. In this exercise, removing the air from the box creates a vacuum, which has a few important implications on phase equilibrium and thermal dynamics.

Firstly, the absence of air drastically reduces the potential for heat transfer since air acts as a medium that conducts heat. This results in extremely limited energy exchanges within the box, maintaining the equilibrium state of 0.00°C.

• The vacuum ensures that no heat enters or leaves the system.
• This contributes to maintaining the balance between ice and water.

Additionally, vacuum systems are crucial in preventing any interactions that would lead to phase changes. In simpler terms, the vacuum acts as a safeguard for maintaining the existing state by providing no avenue for additional heat to enter the system, thereby preventing the melting of ice or freezing of water beyond the natural equilibrium state.