Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 19

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from \(300 \mathrm{~K}\) to \(200 \mathrm{~K}\). (a) Describe how this change might be carried out while keeping the volume of the gas constant. (b) Describe how it might be carried out while keeping the pressure of the gas constant. (c) Does the change in \(\Delta E\) depend on the particular pathway taken to carry out this change of state? Explain.

Short Answer

Expert verified
(a) In an isochoric process, the volume is constant, and the temperature decrease from 300 K to 200 K can be achieved by removing heat from the system. The change in internal energy, ΔE, is given by ΔE = mcΔT. (b) In an isobaric process, the pressure is constant, and the temperature decrease can be achieved by allowing the gas to expand and do work. According to the First Law of Thermodynamics, ΔE = Q - W. (c) The change in internal energy, ΔE, only depends on the initial and final temperatures, not on the particular pathway taken during the change of state. Therefore, ΔE will be the same for both isochoric and isobaric processes.

Step by step solution

01

(a) Isochoric process

In an isochoric process, the volume of the gas remains constant. To decrease the temperature of the gas from 300 K to 200 K at constant volume, we can remove heat from the system. Since the volume is constant, no work is done by the gas, and the heat exchange (Q) is equal to the change in internal energy, ΔE = mcΔT, where m is the mass of the gas, c is the specific heat capacity at constant volume, and ΔT is the change in temperature.
02

(b) Isobaric process

In an isobaric process, the pressure of the gas remains constant while the temperature changes. To achieve a decrease in temperature from 300 K to 200 K at constant pressure, we can allow the gas to expand against an external force, doing work in the process. As the gas loses energy to perform work, its temperature will decrease. So, in this case, both work (W) and heat exchange (Q) are involved. According to the First Law of Thermodynamics, ΔE = Q - W, where Q is the heat added to the system, and W is the work done by the system.
03

(c) Dependence of ΔE on the pathway

The change in internal energy, ΔE, only depends on the initial and final temperatures, and not on the particular pathway taken during the change of state. This is because for an ideal gas, internal energy only depends on the temperature. It doesn't matter if the process is isochoric or isobaric; the change in internal energy will be the same for the same temperature change.

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 \(\mathrm{C}\) to predict how \(\Delta \mathrm{G}^{\circ}\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G^{\circ}\) 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 \(\Delta G^{\circ}\) at \(1000 \mathrm{~K}\). Is the reaction spontaneous under standard conditions at this temperature?

(a) What is meant by calling a process irreversible? (b) After a particular irreversible process, the system is restored to its original state. What can be said about the condition of the surroundings after the system is restored to its original state? (c) Under what conditions will the condensation of a liquid be an irreversible process?

(a) What is the meaning of the standard free-energy change, \(\Delta G^{\circ},\) as compared with \(\Delta G\) ? (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?(c)\) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily occurs rapidly?

Using data from Appendix \(\mathrm{C}\), write the equilibrium-constant expression and calculate the value of the equilibrium constant for these reactions at \(298 \mathrm{~K}\) : (a) \(\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)\) (b) \(2 \mathrm{HBr}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\mathrm{Br}_{2}(g)\) (c) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\)

Use Appendix \(\mathrm{C}\) to compare the standard entropies at \(25^{\circ} \mathrm{C}\) for the following pairs of substances: (a) \(\mathrm{Sc}(s)\) and \(\mathrm{Sc}(g)\), \(\mathrm{NH}_{3}(g)\) and \(\mathrm{NH}_{3}(a q)\) (c) \(1 \mathrm{~mol} \mathrm{P}_{4}(g)\) and \(2 \mathrm{~mol} \mathrm{P}_{2}(g)\), (d) C(graphite) and C(diamond). In each case explain the difference in the entropy values.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

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