A sophomore with nothing better to do adds heat to 0.350 kg of ice at 0.0°C until it is all melted. (a) What is the change in entropy of the water?

Verified step by step guidance

1. Identify the process: The problem involves melting ice at 0°C, which is a phase change from solid to liquid. During this process, the temperature remains constant while the ice absorbs heat.
2. Calculate the heat absorbed (Q) during the melting process: Use the formula Q = m * L_f, where m is the mass of the ice (0.350 kg) and L_f is the latent heat of fusion for ice (approximately 334,000 J/kg).
3. Understand the concept of entropy change (ΔS): Entropy is a measure of disorder or randomness. For a reversible process at constant temperature, the change in entropy is given by ΔS = Q / T, where Q is the heat absorbed and T is the absolute temperature in Kelvin.
4. Convert the temperature to Kelvin: Since the process occurs at 0°C, convert this to Kelvin by adding 273.15, resulting in T = 273.15 K.
5. Calculate the change in entropy (ΔS): Substitute the values of Q and T into the formula ΔS = Q / T to find the change in entropy of the water as the ice melts.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a system that is unavailable for doing work. When heat is added to a system, such as melting ice, the entropy increases as the molecules become more disordered.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. For ice, this is approximately 334,000 J/kg. This energy input is crucial for calculating the change in entropy during the melting process.

Calculating Change in Entropy

The change in entropy (ΔS) when a substance undergoes a phase change can be calculated using the formula ΔS = Q/T, where Q is the heat added and T is the temperature in Kelvin. For melting ice, Q is the product of the mass and latent heat of fusion, and T is the melting point temperature in Kelvin.