A sophomore with nothing better to do adds heat to 0.3500.350 kg of ice at 0.00.0°C until it is all melted. What is the change in entropy of the water?

Ch 20: The Second Law of Thermodynamics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 20: The Second Law of Thermodynamics

Problem 21a

Chapter 20, Problem 21a

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

Verified step by step guidance

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.

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).

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 can be calculated using the formula ΔS = Q / T, where Q is the heat absorbed and T is the absolute temperature in Kelvin.

Convert the temperature from Celsius to Kelvin: Since the process occurs at 0.0°C, convert this to Kelvin by adding 273.15, resulting in T = 273.15 K.

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. When heat is added to a system, such as melting ice, the entropy increases because the molecules become more disordered as they transition from a solid to a liquid state.

Latent Heat of Fusion

The latent heat of fusion is the amount of heat required to change a unit mass of a solid into a liquid without a change in temperature. For ice, this is approximately 334,000 J/kg. This concept is crucial for calculating the heat added to melt the ice, which is necessary to determine the change in entropy.

Thermodynamic Process

A thermodynamic process involves the transfer of heat and work into or out of a system, leading to changes in its state. In this scenario, the process is isothermal, meaning the temperature remains constant at 0°C while the ice melts. Understanding this helps in applying the formula for entropy change, ΔS = Q/T, where Q is the heat added and T is the absolute temperature.

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