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

Giancoli Douglas 5th edition

Ch. 20 - Second Law of Thermodynamics

Problem 38b

Chapter 20, Problem 38b

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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Identify the key concept: The change in entropy of the surroundings is related to the heat exchanged with the surroundings and the temperature at which the exchange occurs. The formula for entropy change is ΔS = -Q/T, where Q is the heat exchanged and T is the absolute temperature.

Determine the heat exchanged (Q): The heat required to convert water to steam at 100°C 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 (L = 2.26 × 10^6 J/kg).

Substitute the values into the formula for Q: Q = (0.45 kg) × (2.26 × 10^6 J/kg). This gives the total heat exchanged during the phase change.

Calculate the temperature in absolute terms: Since the process occurs at 100°C, convert this to Kelvin using T(K) = T(°C) + 273.15. Thus, T = 100 + 273.15 = 373.15 K.

Substitute Q and T into the entropy formula: ΔS_surroundings = -Q/T. Use the value of Q from step 3 and T from step 4 to express the change in entropy of the surroundings.

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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.

Reversible Process

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 thermodynamics, reversible processes are characterized by equilibrium at every stage, allowing for maximum efficiency and the ability to calculate changes in properties like entropy accurately.

Surroundings

In thermodynamics, the surroundings refer to everything outside the system being studied. When analyzing changes in a system, such as the transition of water to steam, it is essential to consider the heat exchange with the surroundings, as this affects the overall entropy change. The surroundings can absorb or release heat, influencing the entropy of both the system and the environment.

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Textbook Question

An ideal heat pump is used to maintain the inside temperature of a house at Tᵢₙ = 22°C when the outside temperature is Tₒᵤₜ. Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by ( 650 W/C°) (Tᵢₙ - Tₒᵤₜ). If the outside temperature is less than you just calculated, what happens?

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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 water, the surroundings, and the universe as a whole. How would your answers differ if the process were irreversible?

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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

What is the coefficient of performance of an ideal heat pump that extracts heat from 6°C air outside and deposits heat inside a house at 24°C?

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