# Comparison of Shaft and Boundary Work

The purpose of

#### power cycles

is to convert heat into work as efficiently as possible.
Recall that areas on PV Diagrams can be interpreted as boundary or shaft work for certain types of systems.

## Closed Systems Internally Reversible Processes

Wb = 0 for constant V Processes

## Open Systems Internally Reversible Processes

SS, SISO, ΔEpot = ΔEkin = 0
for constant P processes
Roll your mouse over this box to close.
Join Learn Thermodynamics Advantage
• Download Data Tables
• Download Study Aids
• Homework problem hints and answers
• Get Help from Dr. B in the LT Blog
• 120 day membership

Get it ALL for \$5 US

### Ch 9, Lesson A, Page 2 - Comparison of Shaft and Boundary Work

• Since we are studying power cycles in this chapter, we need to keep in mind that the goal is to convert heat absorbed from the hot reservoir into work and reject as little heat as possible to the cold reservoir.
• So, heat and work and the equations that let us evaluate them are the keys to this chapter.
• Let’s begin by reviewing relationship between work and areas on PV Diagrams.
• The area under a process path on a PV Diagram is equal to the boundary work per unit mass for an internally reversible process taking place in a closed system.
• This has been drilled into your head over the last few chapters and I hope it has become almost 2nd nature to you now.
• In Lesson 8B, we learned that the area behind or to the left of a process path is equal to minus Ws-dot over m-dot.
• Remember that this equation only applies for internally reversible, steady-state processes that take place in singe-input, single output systems in which changes in kinetic and potential energy are negligible.
• The minus sign appears in this equation because of our sign convention.  As our gas is compressed from 1 to 2, we know that Ws must be negative, right ?  We must put work INTO a compressor to increase the pressure in the working fluid.
• As the pressure increases, dP must be positive and Vhat is always positive.
• So, we need the minus sign to make our sign convention work.
• Now, let’s see how these equations can be applied to thermodynamic cycles.

 Jump to New page Show / Hide Notes