Problem 19 - Chemistry The Central Science In Si Units

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 \(\Delta H\) zero for the process?

Step-by-Step Solution

Answer

(a) The ice cube can melt reversibly at 0°C and 1 atm, with a slow process. (b) \\( abla H\\) is not zero; it equals the heat of fusion.

Step 1: Understand Reversible Process

In thermodynamics, a reversible process is an ideal process that occurs infinitely slowly, allowing the system to remain in equilibrium with its surroundings. For the ice cube to melt reversibly, it must be at thermal equilibrium with a reservoir at 0°C (273.15 K), which is the melting point of ice.

Step 2: Conditions for Reversible Melting

For the ice cube to melt reversibly, the process must occur at a constant temperature of 0°C and at atmospheric pressure (1 atm). Additionally, any heat exchange must happen infinitely slowly to ensure equilibrium is maintained at each stage of melting.

Step 3: Determine if \\( abla H\\) is Zero

The change in enthalpy, \(\Delta H\), is defined as the heat absorbed or released at constant pressure. In the case of the ice cube melting, \(\Delta H\) corresponds to the heat of fusion, which is not zero. Therefore, while the process is reversible, the enthalpy change is not zero because energy is absorbed to break the intermolecular forces in the ice.

Key Concepts

Enthalpy Change

When discussing thermodynamic systems, especially ones involving phase changes like melting, the concept of enthalpy change becomes pivotal. Enthalpy, denoted by the symbol \( H \), represents the total heat content of a system. It changes with heat absorption or release at constant pressure.

In the melting of an ice cube, the enthalpy change \( (\Delta H) \) represents the amount of heat absorbed by the ice to transition from a solid to a liquid without any temperature change. This process occurs under reversible conditions at constant pressure, showing that heat exchange is always involved.

Importantly, the enthalpy change in the melting process of the ice cube can be considered as heat of fusion. This highlights not only the energy absorbed but also the breakage of bonds between water molecules as they transition from solid to liquid. Therefore, when an ice cube melts, \( \Delta H \) is not zero because it measures the energy required to disrupt these intermolecular forces.

Heat of Fusion

The term 'heat of fusion' refers to the heat energy required to change a solid into a liquid at its melting point, without changing its temperature. This concept is vital when studying phase transitions like the reversible melting of an ice cube.

For ice, the heat of fusion is the energy needed to break the rigid structure of the solid ice into the more fluid and dynamic form of liquid water. This energy input is necessary, despite the temperature remaining constant during the entire melting phase.

• The heat of fusion for ice is about 334 J/g. This means for every gram of ice at 0°C, 334 joules of energy are needed to convert it completely into water, while keeping the temperature steady.
• This energy is absorbed to overcome the attraction between water molecules, which holds them in a fixed, crystalline structure in ice.

Thus, even under reversible melting conditions, the heat of fusion indicates that energy input (as heat) is necessary to facilitate the phase change.

Thermal Equilibrium

Understanding thermal equilibrium is crucial for any reversible process in thermodynamics, including the melting of an ice cube. Thermal equilibrium occurs when two systems in thermal contact no longer exchange heat, leading to a uniform temperature.

In the context of our exercise, achieving thermal equilibrium involves the ice cube and the surrounding environment. For the ice to melt reversibly, it must be in a state of thermal equilibrium with a reservoir at 0°C, the melting point of ice. This means that both systems (ice and environment) are at the same temperature, facilitating a stable environment where the melting process can proceed without external thermal disturbances.

• This state ensures any heat exchange between the ice and its surroundings occurs infinitely slowly, aligning with the conditions for a reversible process.
• Reaching thermal equilibrium is vital to allow the melting to happen in a controlled manner without sudden temperature changes that could disrupt the process.

The balance provided by thermal equilibrium ensures that any energy changes necessary for melting are seamlessly integrated into the system, allowing us to better understand the reversible nature of the process.