LectureT6

LectureT6 - Chapter 6 In this chapter we want to continue...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
5/20/2004 H133 Spring 2004 1 Chapter 6 In this chapter we want to continue investigating the concept of entropy. In addition, we will look at ± A new definition of temperature ± The Boltzmann Factor and some applications. Recall back in Chapter 1, we went through a rather detailed discussion of temperature and how to define it through a standard thermoscope. Now we can actually define temperature via entropy ± This is perhaps a much more scientifically satisfying way of defining temperature. Consider two objects A and B that are brought into thermal equilibrium ± They are now in the macropartition with ______________________________________________ ______________________________________________ ± If we consider the case where we hold quantities like V, N, and other macroscopic quantities fix, then the macropartition is completely determined by U A and U B . ± The condition of maximum S TOT can be expressed mathematically by ± Since S TOT is just the sum of S A and S B we have ± Since U B =U – U A 0 = A TOT dU dS 0 ) ( = + = + = A B A A A B A A TOT dU dS dU dS dU S S d dU dS B B B B A B B B A B dU dS dU dS dU dU dU dS dU dS = = = ) 1 (
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5/20/2004 H133 Spring 2004 2 Definition of Temperature Taking the last two expressions and combining them we find Each condition (they are the same…just different forms) is the condition that two objects are in thermal equilibrium. ± The first form says that the two objects are in thermal equilibrium when the two slopes relative to U A (or U B ) are equal in magnitude but opposite in sign. ² Graphically this can be seen as: ± In the second form we are determining the derivative of each object’s entropy with respect to its own U…there is no reference to the other object. ² The place where these two derivatives are equal we have thermal equilibrium. But the Zeroth Law of Thermodynamics says when two objects are in thermal equilibrium they are at the same temperature. B B A A A B A A dU dS dU dS dU dS dU dS = = U A Entropy S TOT S A S B
Background image of page 2
5/20/2004 H133 Spring 2004 3 Temperature This last reminder of the 0 th Law of Thermodynamics implies that the derivative should be related to the temperature is some way Note that the choice of f(T) is somewhat arbitrary however, it must have the following characteristic
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

LectureT6 - Chapter 6 In this chapter we want to continue...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online