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Ch. 20 - Second Law of Thermodynamics
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 20 - Second Law of ThermodynamicsProblem 38d
Chapter 20, Problem 38d

If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the water, the surroundings, and the universe as a whole. How would your answers differ if the process were irreversible?

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Step 1: Understand the problem. The problem involves a phase change of water at constant temperature (100°C) from liquid to steam. This is an isothermal process, and the change in entropy (ΔS) can be calculated using the formula ΔS = Q/T, where Q is the heat added and T is the absolute temperature in kelvins.
Step 2: Calculate the heat added (Q). The heat required for the phase change is given by Q = mL, where m is the mass of the water (0.45 kg) and L is the latent heat of vaporization of water (approximately 2.26 × 10^6 J/kg). Substitute the values to find Q.
Step 3: Calculate the change in entropy of the water (ΔS_water). Use the formula ΔS = Q/T, where T is the absolute temperature in kelvins (100°C = 373 K). Substitute the value of Q from Step 2 and T = 373 K to find ΔS_water.
Step 4: Analyze the surroundings and the universe. For a reversible process, the heat lost by the surroundings is equal in magnitude but opposite in sign to the heat gained by the system. Therefore, the entropy change of the surroundings (ΔS_surroundings) is -Q/T. The total entropy change of the universe (ΔS_universe) is the sum of ΔS_water and ΔS_surroundings, which is zero for a reversible process.
Step 5: Consider the irreversible process. In an irreversible process, the entropy change of the system (ΔS_water) remains the same, but the entropy change of the surroundings (ΔS_surroundings) is not equal in magnitude to -Q/T. This results in a positive total entropy change for the universe (ΔS_universe > 0), reflecting the second law of thermodynamics.

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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 system that is not available to do work. When a substance undergoes a phase change, such as from water to steam, the entropy of the system changes, reflecting the increased disorder as molecules move from a liquid to a gaseous state.
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Reversible and Irreversible Processes

A reversible process is an idealized process that occurs in such a way that the system and surroundings can be returned to their original states without any net change. In contrast, an irreversible process cannot be reversed without leaving changes in the system and surroundings, often resulting in increased entropy. The distinction is crucial for calculating changes in entropy, as reversible processes yield maximum efficiency and minimum entropy change.
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Surroundings and Universe in Thermodynamics

In thermodynamics, the surroundings refer to everything outside the system being studied, while the universe encompasses both the system and its surroundings. When analyzing entropy changes, it is essential to consider how energy is exchanged between the system and its surroundings, as this affects the overall entropy of the universe. The total change in entropy for the universe helps determine the spontaneity of a process.
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Related Practice
Textbook Question

Why would you expect the total entropy change in a Carnot cycle to be zero? Do a calculation to show that it is zero.

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Textbook Question

Why would you expect the total entropy change in a Carnot cycle to be zero?

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Textbook Question

If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the universe as a whole.

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Textbook Question

If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the surroundings.

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Textbook Question

How much less per year would it cost a family to operate a heat pump that has a coefficient of performance of 2.9 than an electric heater that costs \$2100 to heat their home for a year? If the conversion to the heat pump costs \$15,000, how long would it take the family to break even on heating costs? How much would the family save in 20 years?

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Textbook Question

A general theorem states that the amount of energy that becomes unavailable to do useful work in any process is equal to TL∆S, where TL is the lowest temperature available and ∆S is the total change in entropy during the process. Show that this is valid in the specific cases of a falling rock that comes to rest when it hits the ground.