The Clausius Inequality

Ch 7, Lesson A, Page 2 - The Clausius Inequality

• Well, there it is, the Clausius Inequaltiy.
• It’s a nice short equation, but it has two or three parts that can be confusing.
• First of all, it is an inequality.  Those are never as easy to deal with as an equality.  But, I think we can manage.
• Next, you notice the crazy looking integral symbol.  That is the symbol for a cyclic integral.  It just means that we evaluate the integral over an entire series of processes or steps that lead back to the original state of the system.
• That is to say, a cyclic integral must be evaluated over an entire cycle.  No problem, right ?
• The last issue is the squiggly d that is in front of the Q.  This is the symbol for an inexact differential.
• You may recall from Lesson 4B, that heat and work are path functions.  As a result, the differentials of Q and W are inexact.  This means that the integral of dQ from state 1 to state 2 may be different if the system moves along a different process path from state 1 to 2.
• If I haven’t refreshed your memory adequately, review Lessons 4A and 4B and then return to this page.
• OK, so I hope we are comfortable with the fact that this equation includes a cyclic integral, an inexact differential and that it is an inequality.
• Now, let’s see if we can figure out WHY this equation is true.