Question

Several ice cubes are placed in a beaker on a lab bench, and their temperature, initially at \(-5.0^{\circ} \mathrm{C}\), is monitored. Explain what happens to the temperature as a function of time. Make a sketch of how the temperature might change with time. (Assume that the lab is at \(25^{\circ} \mathrm{C}\).)

Short answer

The temperature rises from -5.0^{ circ} C to 0^{ circ} C, remains constant at 0^{ circ} C as the ice melts, and then continues to rise until reaching the lab temperature of 25^{ circ} C.

Step-by-step solution

Understand the Initial Condition

The ice cubes are at a temperature of -5.0^{ circ} C, which is below the freezing point of water (0^{ circ} C). The lab environment is at 25^{ circ} C, which is the temperature the ice will eventually reach if given enough time.

Temperature Increase to 0^{ circ} C

As time progresses, the temperature of the ice will increase due to the heat transfer from the warmer air in the lab. This warming will continue until the ice reaches 0^{ circ} C, the melting point of ice.

Phase Change at 0^{ circ} C

At 0^{ circ} C, the ice begins to melt, transforming from solid to liquid. During this phase change, the temperature will remain constant at 0^{ circ} C despite continued heat absorption, as the energy is used to break the intermolecular bonds rather than increasing the temperature.

Temperature Increase after Melting

Once all the ice has melted into liquid water, the temperature of the water will begin to rise again. The warming will continue until it equilibrates with the lab temperature, assuming no other heat losses or gains.

Sketch the Temperature-Time Graph

The temperature-time graph would show a curve where the temperature increases steadily from -5.0^{ circ} C to 0^{ circ} C, then a horizontal line at 0^{ circ} C during the melting phase, followed by a steady rise again until it reaches 25^{ circ} C.

Key concepts

Heat Transfer

Heat transfer is the movement of thermal energy from one object or medium to another. It's the underlying mechanism that causes ice cubes in a beaker to increase in temperature when in a warm room. The three modes of heat transfer are conduction, convection, and radiation. In this scenario, conduction and convection are most pertinent, as the warmer air (at 25°C) surrounding the ice cubes (initially at -5°C) transfers heat to the colder ice through the air and the beaker.

This transfer will continue until thermal equilibrium is reached, meaning the ice and surrounding environment eventually stabilize at the same temperature. However, during a phase change, all the heat being transferred is used to break intermolecular bonds, a process requiring energy but not resulting in a temperature increase, which leads to a unique plateau on the temperature-time graph known as the latent heat of fusion.

Students often have difficulty grasping why the temperature does not change during a phase change. To enhance understanding, one may consider that all the energy absorbed is consumed in rearranging the molecular structure, from solid to liquid in the case of ice melting, rather than speeding up molecular motion which would manifest as a temperature increase.

Melting Point of Ice

The melting point of a substance is the temperature at which it changes state from solid to liquid. For ice, this occurs at 0°C under standard atmospheric conditions. At this point, known as the melting point, the thermal energy being transferred to the ice is used to break the intermolecular bonds that hold water molecules in a solid structure.

This absorption of energy without an increase in temperature is because the energy is not increasing the kinetic energy of the molecules (which would raise the temperature), but rather it is being utilized to overcome the attractive forces that maintain ice's rigid, crystalline structure. Consequently, during the phase change from ice to water, there is a plateau on the temperature-time graph where the temperature remains constant despite continuous heat transfer. This concept can be counterintuitive for students, but it's pivotal for understanding heat transfers during phase changes.

Temperature-Time Graph

A temperature-time graph is a visual representation of the change in temperature of a substance over time. Such a graph effectively illustrates how the temperature of the ice cubes changes as they're exposed to a warmer environment. From the initial condition at -5°C, the graph will display a steady increase in temperature as the ice absorbs heat. However, upon reaching the melting point (0°C), a horizontal flat line depicts the phase change, showcasing that temperature doesn't increase while the ice melts.

After the ice has completely turned to liquid water, the temperature begins to rise once more, until it reaches equilibrium with the room temperature. The graph provides a clear visualization of these key stages: initial warming, phase change, and final warming. This graphical representation helps students to conceptualize and retain the distinct processes occurring during heat transfer and phase changes.

Intermolecular Bonds

Intermolecular bonds are the forces that hold molecules together, and are pivotal in understanding the phase changes that occur in substances like ice. These bonds can be hydrogen bonds, van der Waals forces, or dipole-dipole interactions among others. In ice, water molecules are held together in a crystalline structure by hydrogen bonds, which are relatively strong intermolecular bonds.

When heat is transferred to the ice, its molecular energy increases until it's sufficient to break these hydrogen bonds, allowing the molecules to move freely and the ice to transform into liquid. It's this breaking of intermolecular bonds that characterizes the melting process. The amount of energy required to accomplish this is significant, which is why the temperature remains constant during the melting point and why a significant amount of time can be observed on the temperature-time graph where no temperature change occurs, despite ongoing heat absorption.