Skip to main content
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 38c
Chapter 20, Problem 38c

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.

Verified step by step guidance
1
Identify the key concept: The problem involves a phase change (water to steam) at constant temperature, which is an isothermal process. The change in entropy of the universe is the sum of the entropy changes of the system (water) and the surroundings.
Calculate the entropy change of the system (water): Use the formula \( \Delta S_{\text{system}} = \frac{Q}{T} \), where \( Q \) is the heat absorbed during the phase change and \( T \) is the absolute temperature. The heat \( Q \) can be calculated using \( Q = mL \), where \( m \) is the mass of the water and \( L \) is the latent heat of vaporization of water.
Substitute the known values: \( m = 0.45 \; \text{kg} \), \( L = 2.26 \times 10^6 \; \text{J/kg} \), and \( T = 100 + 273.15 = 373.15 \; \text{K} \). Compute \( Q \) and then use it to find \( \Delta S_{\text{system}} \).
Determine the entropy change of the surroundings: Since the process is reversible, the heat lost by the surroundings is equal in magnitude but opposite in sign to the heat gained by the system. Thus, \( \Delta S_{\text{surroundings}} = -\frac{Q}{T} \), where \( T \) is the same temperature as the system.
Add the entropy changes: The total entropy change of the universe is \( \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \). For a reversible process, these two terms cancel out, resulting in \( \Delta S_{\text{universe}} = 0 \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

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 increases due to the greater disorder in the gaseous state compared to the liquid state.
Recommended video:
Guided course
07:50
Intro to Entropy

Reversible Process

A reversible process is an idealized process that occurs in such a way that the system and its 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 state variables, such as entropy, accurately.
Recommended video:
Guided course
08:45
Properties of Cyclic Thermodynamic Processes

Change in Entropy of the Universe

The change in entropy of the universe is the sum of the changes in entropy of the system and its surroundings. According to the second law of thermodynamics, the total entropy of the universe tends to increase over time. In the context of the given problem, calculating the change in entropy involves considering both the entropy change of the water turning into steam and the heat exchanged with the surroundings during the process.
Recommended video:
Guided course
06:20
Calculating Entropy Changes for Systems of Objects
Related Practice
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?

2
views
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.

1
views
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?

2
views
Textbook Question

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

1
views
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.

1
views
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?

2
views