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.

To allow the ice cube to melt reversibly, the melting process must occur under thermodynamic equilibrium. This means: 1. The temperature of the ice cube should be equal to its melting point (0°C or 273.15 K) 2. The pressure applied on the ice cube must be equal to the atmospheric pressure (around 1 atm or 101325 Pa) In conclusion, the ice cube can melt reversibly when it is at its melting point and the pressure is constant (at atmospheric pressure).

In order to determine if the change in internal energy (∆E) is zero during a reversible melting process, we can use the first law of thermodynamics, which states: ∆E = Q - W Where: - ∆E is the change in internal energy of the system - Q is the heat added to the system - W is the work done by the system During a constant-pressure reversible melting process, the ice cube absorbs heat (Q) at its melting point, which is used to break the hydrogen bonds within the ice. Simultaneously, the volume of the ice cube changes as the ice transforms into liquid water. This change in volume results in work done by the ice cube (W). Since both heat is absorbed and work is done by the ice cube, it implies that the energy is transferred within the system. Therefore, we can conclude that the change in internal energy (∆E) is NOT zero for the reversible melting process of the ice cube.