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

A process can be considered reversible if it proceeds infinitesimally slowly, maintaining thermodynamic equilibrium between the system (ice cube) and its surroundings throughout the entire process. For the ice cube to melt reversibly, it must be heated at the same rate it is melting, keeping the system and surroundings in equilibrium. Let's consider an ice cube at its melting point, which is 0°C (273.15 K) at atmospheric pressure. To make the melting process reversible, the temperature of the surroundings should be infinitesimally higher than the melting point. This will provide a gradual supply of heat to the ice cube, allowing it to melt slowly while maintaining equilibrium with its surroundings.

Enthalpy change, \(\Delta H\), is the amount of heat absorbed or released during a process at constant pressure. In the case of the ice cube melting, it absorbs heat from its surroundings, which is converted into internal energy, leading to a phase transition from solid to liquid. The enthalpy change for melting is also known as the enthalpy of fusion, which is the amount of heat required to convert 1 mole of a substance from the solid phase to the liquid phase at its melting point and constant pressure. For water, the enthalpy of fusion is approximately 6.01 kJ/mol. As the ice cube is absorbing heat to transform from solid to liquid during the reversible melting process, the enthalpy change, \(\Delta H\), is positive and non-zero.

To sum up, an ice cube can melt reversibly if it is heated infinitesimally slowly, maintaining thermodynamic equilibrium between the system (ice cube) and its surroundings. The surroundings should have a temperature infinitesimally higher than the melting point of the ice cube (0°C or 273.15 K). During the reversible melting process, the enthalpy change, \(\Delta H\), is positive and non-zero, since the ice cube absorbs heat to transform from solid to liquid.