{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ME 2124 Work

# ME 2124 Work - = = = âˆ âˆ 1 2 1 1 2 1 1 1 2 1 12 ln V V V...

This preview shows page 1. Sign up to view the full content.

ME 2124 Fall 2011 © Al Kornhauser Pressure-Volume Work for Closed Systems Pressure-volume work done on the environment by a system going from state 1 to state 2 is defined by = 2 1 12 PdV W . This definition gives work out of the system as positive. It is only valid when the process is quasistatic, so that the system is at uniform pressure during each step of the process. In many real processes this equation cannot be integrated in closed form. For some machines – steam engines, internal combustion engines, and reciprocating compressors – pressure and volume data from tests is often numerically integrated to determine work. For a few simple but important cases the integral can be calculated analytically. Constant volume: 0 2 1 12 = = PdV W Constant pressure: ( ) 1 2 2 1 12 V V P PdV W - = = Constant temperature ideal gas:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = = = âˆ« âˆ« 1 2 1 1 2 1 1 1 2 1 12 ln V V V P dV V V P PdV W = = 1 2 1 2 2 2 ln ln V V mRT V V V P Polytropic ( PV n = const.) ideal gas: ( ) n V V V P dV V V P PdV W n n n n n--= = =--âˆ« âˆ« 1 1 1 1 2 1 1 2 1 1 1 2 1 12 ( ) ( ) n V P V P n V V P V V P n n n n--=--=--1 1 1 1 2 2 1 1 1 1 1 2 2 2 ( ) n T T mR--= 1 1 2 For any quasistatic process in a closed system, the work is proportional to the area under the curve of a pressure-volume diagram. If volume is increasing during the process (1 to 2 on the figure at right) work will be positive, while if it is decreasing (2 to 1 on the figure) it will be negative. P V W 1 2...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern