2.0 kg of ice melts completely into liquid water at 0^∘ C. (a) The change in entropy of the ice

step 1 Let us solve the first part of this problem. Here we need to find whether the change in entropy

2.0 kg of ice melts completely into liquid water at 0^∘ C....

$2.0 \mathrm{~kg}$ of ice melts completely into liquid water at $0^{\circ} \mathrm{C}$. (a) The change in entropy of the ice (water) in this process is (1) positive, (2) zero, (3) negative. Explain. (b) What is the change in entropy of the ice (water)?

Key Concepts

Reversible Process and Entropy Change Calculation

For a process occurring at a constant temperature, such as the melting of ice at 0°C, the entropy change can be calculated using the equation ?S = Q/T, where Q is the heat absorbed (in this case, the latent heat of fusion multiplied by the mass of the substance) and T is the absolute temperature. Since the process is effectively reversible at the phase change temperature, the positive value of ?S confirms the thermodynamic prediction of increasing disorder.

Entropy

Entropy is a thermodynamic property representing the degree of disorder or randomness in a system. When a substance undergoes a phase change, such as melting, the structure reorganizes and typically becomes more disordered, leading to an increase in entropy.

Phase Transition (Melting)

During the melting process, a solid transforms into a liquid at its melting temperature. This phase transition involves an increase in randomness because the molecules in a liquid are less orderly than those in a solid, which results in a positive change in entropy.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy required per unit mass to convert a solid into a liquid at its melting point without changing its temperature. This energy input increases the internal energy of the system, contributing to the increase in entropy during melting.

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