# Work to Create a Vacuum

1. May 25, 2014

### kearneytj

I'm trying to determine the amount of work required to create a vacuum. The vacuum will be within a one cubic meter tube with a pressure of 56,777 Pascals. A pneumatic cylinder will be used to remove the air from the tube to create the vacuum.

The standard formula for the work to create a vacuum is: Work = Pressure Difference x Volume. However, I've read in other posts that when considering the use of a cylinder and piston there is actually some work that can be reclaimed since the piston and cylinder provides additional volume for the exhausted gas to expand into. Therefore, the correct formula to calculate work assuming an ambient atmospheric pressure of 101,325 Pascals is as follows:

W = V * ( Pambient - Pnew ) + V * Pnew * natural log(Pnew/Pambient)

Using the above formula I get:

W = 1 cubic meter * (101,325 Pascals - 56,777 Pascals) + 1 cubic meter * 56,777 Pascals * -.579197

W = 11,674 Joules

Could someone please validate that I've correctly calculated the work required to create a vacuum using a pneumatic cylinder?