Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 22

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

Short Answer

Expert verified
a) True. The entropy of the universe increases for any spontaneous process. b) False. The entropy change of the system is not equal and opposite that of the surroundings for any irreversible process. c) False. The entropy of the system doesn't always increase in a spontaneous process. d) True. The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

Step by step solution

01

Statement a) Entropy for spontaneous processes

The second law of thermodynamics states that the total entropy of the universe tends to increase in spontaneous processes. Based on this principle, statement a) is true. The entropy of the universe increases for any spontaneous process.
02

Statement b) Entropy change for irreversible processes

For an irreversible process, the entropy change of the system is not equal and opposite to that of the surroundings. In fact, the total entropy change of the universe (system and surroundings combined) is greater than zero in an irreversible process, which means that the entropy of the system and surroundings both increase. Statement b) is false.
03

Statement c) Entropy increase in spontaneous processes

For a process to be spontaneous, the total entropy change of the universe (system and surroundings combined) must be greater than zero. However, it doesn't mean that the entropy of the system itself must always increase. In some spontaneous processes, the entropy of the system may decrease, but the entropy of the surroundings increases enough such that the total entropy change remains positive. Therefore, statement c) is false.
04

Statement d) Entropy change for isothermal processes

For an isothermal process, the temperature remains constant, and the entropy change is given by \(\Delta S = \int \frac{dq}{T}\), where dq is the infinitesimal heat exchange, and T is the constant absolute temperature. So, the entropy change for an isothermal process indeed depends on both the absolute temperature and the amount of heat reversibly transferred. Statement d) is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

The crystalline hydrate $\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s)$ loses water when placed in a large, closed, dry vessel at room temperature: $$ \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) $$ This process is spontaneous and \(\Delta H^{\circ}\) is positive at room temperature. (a) What is the sign of \(\Delta S^{\circ}\) at room temperature? (b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does \(\Delta S^{\circ}\) change for this reaction at room temperature?

Consider the reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ (a) Using data from Appendix \(\mathrm{C},\) calculate \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\). (b) Calculate \(\Delta G\) at \(298 \mathrm{~K}\) if the partial pressures of all gases are \(33.4 \mathrm{kPa}\).

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\( in body tissue produces \)\mathrm{CO}_{2}$ and \(\mathrm{H}_{2} \mathrm{O} .\) In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\( and \)\mathrm{CO}_{2}$. (a) Using data given in Appendix \(\mathrm{C}\), compare the equilibrium constants for the following reactions: $$ \begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(I)+2 \mathrm{CO}_{2}(g) \end{array} $$ (b) Compare the maximum work that can be obtained from these processes under standard conditions.

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0,\) and \(w=0 .\) (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. \((\mathbf{c})\) What is the "driving force" for the expansion of the gas: enthalpy or entropy?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Inorganic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free