Problem 19 - Chemistry: The Central Science

Question

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta E\) zero for the process? Explain.

Step-by-Step Solution

Answer

For an ice cube to melt reversibly, it must occur under slow, equilibrium conditions with the surrounding temperature slightly above 0°C, and constant pressure. If the ice cube melts reversibly, the change in internal energy (\(\Delta E\)) is zero since in an idealized reversible process, both the heat transferred and the work done on the system are zero.

Step 1: Understanding reversibility in thermodynamics

A process is considered to be reversible if it can be reversed by an infinitesimally small change in the system's conditions. Reversible processes are ideal processes in which no energy is lost to the surroundings as heat, and the system is always in equilibrium with its surroundings. In real-world situations, no process is perfectly reversible, as there is always some energy lost as heat. However, we can still consider the ideal conditions to analyze the theoretical aspects of reversible processes.

Step 2: Analyzing the conditions for the ice cube to melt reversibly

For an ice cube to melt reversibly, the process must occur in equilibrium with its surroundings. This means that we need to consider the following conditions: 1. The system (ice cube) and surroundings should exchange energy in the form of heat so slowly that the system remains in equilibrium throughout the entire process. 2. The surrounding temperature should be slightly above the melting point of ice, which is 0°C (273.15 K) at atmospheric pressure. Essentially, this means that there must be a tiny temperature gradient between the system and its surroundings. 3. The pressure acting on the ice cube should remain constant throughout the process since changes in pressure can also affect phase transitions and disrupt reversible equilibrium.

Step 3: Determining if the change in internal energy is zero for the reversible process

To determine whether the change in internal energy (\(\Delta E\)) is zero or not for the reversible process, we can refer to the first law of thermodynamics, which states: \( \Delta E = Q + W \) Here, \( \Delta E \) is the change in internal energy, \(Q\) is the heat added to the system, and \(W\) is the work done on the system. In a reversible process, the heat is transferred slowly and gradually so that the temperature change remains infinitesimally small. Assuming we are dealing with an idealized situation in which the system is in perfect equilibrium, the work \(W\) done on the system will be zero. Consequently, if the system remains in equilibrium, any heat exchanged with the surroundings will be equally compensated, leading to \(Q = 0\). Since both the heat transferred and the work done are zero in this idealized reversible process, we can conclude that \( \Delta E = 0 \) for the reversible melting of the ice cube.

Step 4: Summary and Conclusion

In summary, for a system consisting of an ice cube to melt reversibly, the melting process must occur under very slow, equilibrium conditions with the surrounding temperature slightly higher than the ice's melting point and constant pressure. Under these idealized conditions, the change in internal energy, \(\Delta E\) is zero for the process. This is because there will be no work done on the system, and any heat exchanged with the surroundings will balance out.

Key Concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which dictate physical laws that describe the nature of energy and how it relates to various physical processes.

In the context of melting ice, thermodynamics allows us to understand how energy transfer—as heat—causes the ice to change from a solid to a liquid. Energy in the form of heat is absorbed by the ice from its surroundings leading to a phase change. Throughout this process, the laws of thermodynamics are observed to ensure energy conservation and to dictate the directionality of heat flow.

First Law of Thermodynamics

The first law of thermodynamics, also known as the principle of the conservation of energy, states that energy cannot be created or destroyed in an isolated system. The energy within a closed system is constant, unless it's changed by adding or removing work or heat. It's expressed in the equation,\[ \Delta E = Q + W \]where \( \Delta E \) is the change in internal energy of the system, \( Q \) is the heat added to or subtracted from the system, and \( W \) is the work done by or on the system.

In the reversible melting of ice, if we consider the system to be isolated from the environment or the process to be occurring in such a way that it maintains perfect equilibrium, any heat absorbed by the melting ice (\[ Q \]) is compensated for by work (\[ W \]) done by the surrounding environment (like atmospheric pressure). If the work and heat transfer are balanced such that the net energy change is zero, then \( \Delta E \) will also be zero, abiding by the first law of thermodynamics.

Phase Transition

A phase transition is the transformation of a substance from one state of matter to another. Common transitions include the melting of ice to water (solid to liquid), the boiling of water to steam (liquid to gas), and the condensation of steam to water (gas to liquid). At the molecular level, a phase transition involves an energy exchange that alters the bonds between molecules, hence changing its state.

In the case of ice melting, which is our focus, this transition occurs at the melting point under equilibrium conditions. The amount of heat required to change the phase of a unit mass of a substance is known as the latent heat of transformation. Reversible melting signifies that the process can proceed forwards (melting) and backwards (freezing) under ideal, equilibrium conditions, without losing any total energy in the system or changing the inherent properties of the substance.