Prev. Article Next Article Table of Contents

Article

Why Do Two Objects at Different Temperatures Come to a Common Intermediate Temperature When Put in Contact? Entropy Is Maximized.

Your current credentials do not allow retrieval of the full text.

Purchase the full-text

PDF/HTML,
figures/images,
references and tables,
(where available)

Eric A. Gislason

Department of Chemistry, University of Illinois at Chicago, Chicago, IL, 60680

Norman C. Craig

Department of Chemistry, Oberlin College, Oberlin, OH, 44074

J. Chem. Educ., 2006, 83 (6), p 885

DOI: 10.1021/ed083p885

Publication Date (Web): June 1, 2006

Section:

History, Education, and Documentation

Abstract

A classic problem in thermodynamics is to place two objects with different heat capacities and different temperatures in thermal contact and ask what is the final common temperature. Normally, this temperature is found using the first law of thermodynamics. A single, intermediate final temperature is an assumption (from experience) that is not required by the first law. Why is the final temperature of the two objects at equilibrium the same? It is shown that this outcome is a consequence of the second law of thermodynamics subject to the constraint of energy conservation (the first law). That is, the overall entropy of the universe is maximized when the two objects reach a common temperature. The analysis is extended to the case of two different samples of ideal gas at different pressures as well as different temperatures placed in mechanical (for example, by placing a moveable piston between the gases) and thermal contact. In this case, it is shown that the two gases at equilibrium reach a common temperature as well as a common pressure.

Keywords (Audience):

Graduate Education / Research

Keywords (Domain):

Physical Chemistry

Keywords (Pedagogy):

Problem Solving / Decision Making

Keywords (Subject):

Calorimetry / Thermochemistry

View: Hi-Res PDF | PDF w/ Links

Citing Articles

View all 5 citing articles

Citation data is made available by participants in CrossRef's Cited-by Linking service. For a more comprehensive list of citations to this article, users are encouraged to perform a search in SciFinder.

This article has been cited by 5 ACS Journal articles (5 most recent appear below).

The “Global” Formulation of Thermodynamics and the First Law: 50 Years On
Eric A. Gislason and Norman C. Craig
Journal of Chemical Education2011 88 (11), 1525-1530
- The “Global” Formulation of Thermodynamics and the First Law: 50 Years On
  Eric A. Gislason and Norman C. Craig
  Journal of Chemical Education2011 88 (11), 1525-1530
  Nearly 50 years ago, Henry Bent published his groundbreaking article in this Journal introducing the “global” formulation of thermodynamics. In the following years, the global formulation was elaborated by Bent and by one of the present authors. The ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links
Understanding Chemical Equilibrium Using Entropy Analysis: The Relationship Between ΔS_tot(sys^o) and the Equilibrium Constant
Thomas H. Bindel
Journal of Chemical Education2010 87 (7), 694-699
- Understanding Chemical Equilibrium Using Entropy Analysis: The Relationship Between ΔS_tot(sys^o) and the Equilibrium Constant
  Thomas H. Bindel
  Journal of Chemical Education2010 87 (7), 694-699
  Entropy analyses as a function of the extent of reaction are presented for a number of physicochemical processes, including vaporization of a liquid, dimerization of nitrogen dioxide, and the autoionization of water. Graphs of the total entropy change ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links
Combining Chemistry and Music To Engage Students’ Interest. Using Songs To Accompany Selected Chemical Topics
Arthur M. Last
Journal of Chemical Education2009 86 (10), 1202
- Combining Chemistry and Music To Engage Students’ Interest. Using Songs To Accompany Selected Chemical Topics
  Arthur M. Last
  Journal of Chemical Education2009 86 (10), 1202
  The use of recorded music to add interest to a variety of lecture topics is described. Topics include the periodic table, the formation of ionic compounds, thermodynamics, carbohydrates, nuclear chemistry, and qualitative analysis.
  Abstract | Hi-Res PDF | PDF w/ Links
Zeroth Law, Entropy, Equilibrium, and All That
Sebastian G. Canagaratna
Journal of Chemical Education2008 85 (5), 732
- Zeroth Law, Entropy, Equilibrium, and All That
  Sebastian G. Canagaratna
  Journal of Chemical Education2008 85 (5), 732
  The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced ...
  Abstract | Hi-Res PDF | PDF w/ Links
Pressure–Volume Integral Expressions for Work in Irreversible Processes
Eric A. Gislason , Norman C. Craig
Journal of Chemical Education2007 84 (3), 499
- Pressure–Volume Integral Expressions for Work in Irreversible Processes
  Eric A. Gislason , Norman C. Craig
  Journal of Chemical Education2007 84 (3), 499
  Different formulations of thermodynamic work w as a pressure–volume integral are examined for a piston moving against a gas in an irreversible process. Proper expressions are obtained using the instantaneous pressure of the gas on the piston as the ...
  Abstract | Hi-Res PDF | PDF w/ Links