# Intro to Entropy Balances on Open Systems

In the previous lesson, we studied

#### entropy balances

on closed systems. That was interesting, but not broadly applicable. In this lesson, we will begin by deriving the

#### entropy balance for open systems

. We will then show how it can be simplified for steady-state (SS) and single-inlet, single-outlet (SISO) processes.
Next, we will consider the significance of the area under an internally reversible (Int Rev) process path on a TS Diagram for an open system and use the result to help us derive the

#### Mechanical Energy Balance Equation

(MEBE). One special case of the MEBE is the

#### Bernoulli Equation

, which applies when Ws = 0.
In many processes of interest in this course, changes in Epot and Ekin are negligible. This situation yields another special case of the MEBE that we will apply to all of the polytropic processes that we introduced in Lesson 7E.
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### Ch 8, Lesson B, Page 1 - Intro to Entropy Balances on Open Systems

• In this lesson, we will develop the integral form of the entropy balance equation for open systems.
• This equation is long and messy, just like the general form of the 1st Law for open systems.
• How did we deal with the 1st Law for open systems ?  We simplified it whenever we could and we are going to do the same thing with the entropy balance for open systems.
• Common simplifications apply for steady-state processes and SISO processes, that is processes with only one stream entering and one stream leaving the system.
• The next most popular simplification applies when the process under consideration is internally reversible.
• This assumption lets us use the Gibbs Equations to derive the Mechanical Energy Balance Equation starting from the 1st Law.
• In the kinds of processes that make up thermodynamic cycles, changes in kinetic and potential energy are often negligible.
• This let’s us simplify the Mechanical Energy Balance Equation to the form that we will use to analyze all of the polytropic processes that we introduced back in lesson 7E.
• The result of this analysis of polytropic processes is a set of equations that will allow us to calculate the non PV work produced or consumed based only on the P, V-hat and T of the initial and final states and the value of d for the polytropic process.
• The set of equations will include equations for real fluids and for ideal gases.
• So, why is this important ?
• Well, in this course, we don’t often deal with electrical, magnetic or any exotic type of work.
• Basically, we deal with boundary work, PV work and shaft work.
• In most open systems, there isn’t any boundary work because the size of the system doesn’t change.
• So, when we talk about non-PV work, we usually mean shaft work.
• So, the equations we will develop in this lesson will let us calculate the shaft work for all of our favorite polytropic processes.
• That is so cool because shaft work and heat transfer are the two things we are most interested in when we analyze an open system.
• The only catch is that we had to make many assumptions about our processes in order to arrive at these equations.
• Nonetheless, the results are very, very useful.
• Well, hopefully I have convinced you that this is one of the most important lessons in the course, so let’s dive right in.

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