Entropy Generation: The Heart of the Matter

Ch 7, Lesson C, Page 3 - Entropy Generation: The Heart of the Matter

• Because dS is associated with the MAXIMUM value of dQ over T, we must ADD something to the value of dQ over T that we get from any real, irreversible path in order to make the two equations at the top of the page into equalities.
• We call this quantity entropy generation and use the symbol S sub g-e-n.
• In the differential form of the general entropy inequality, we must add δSgen.
• But, why did I use a squiggly “d” here ?
• Because Sgen is a path variable and therefore has an inexact differential.
• How do we know Sgen is a path variable.
• Well, Sgen is just the value you get for the integral of dQ over T along an internally reversible path MINUS the value you get for the integral of dQ over T along the ACTUAL path your process follows.
• Whenever a process follows a different path, it makes sense that the integral of dQ over T would turn out to have a different value, right ? As a result, Sgen also has a different value.
• So, you see that the value we get for Sgen DOES depend on the process path.  Therefore, Sgen is a path variable and has an inexact differential. Whew.  What else can we figure out about Sgen?
• Well, we know that Sgen is always a positive number because the internally reversible path ALWAYS yields the highest value for the integral of dQ over T.
• The last observation is the kicker.
• The more irreversible the process, the larger the value of Sgen.
• So, processes with lots of friction, rapid expansion or compression of fluid or heat transfer through a big temperature difference are MORE irreversible and result in larger values for Sgen.
• This is a HUGE result.  Sgen gives us a way to QUANTIFY the performance of an individual process by telling us how close the process approximates a reversible process.
• We will discuss this much more in Chapter 8.
• The equations in the box tell us one more important thing about entropy.  It is NOT conserved.
• Mass and energy are conserved.  They cannot be created or destroyed.
• Entropy can be created.  In fact entropy is created by ALL REAL PROCESSES because Sgen is always positive !
• Cool, eh ? Now, let’s see what this means when we start plotting process paths on our trusty TS Diagrams.