Steam Engine work application problem

[8point1]

Homework Statement

In a steam engine the pressure and volume of steam satisfy the equation PV^1.4=k, where k is a constant. Calculate the work done by the engine (in ft/lbs) during a cycle when the steam starts at a pressure of 100 lb/in² and a volume of 400in³ and expands to a volume of 1100in³.

Homework Equations

Use the fact that the work done by the gas when the volume expands from volume v₁ to volume v₂ is:

W=∫V2v1 P dV

The Attempt at a Solution

As usual, getting hung up on where to start. So I tried to find k. Solving for k at the starting pressure of 100lb/in² and volume of 400in³ I get a k=439,424.2

That # seems way high. Is the problem assuming the pressure is starting at these values (100lb/in² and 400in³)??

Thanks

 

[SteamKing]

You might want to review this article:
http://en.wikipedia.org/wiki/Adiabatic_process

 

[8point1]

interesting... now I'm even more confused!

 

[8point1]

Our professor didn't say we needed any special formulas or anything - that we should know how to do this from our previous section's lessons. Where do I start? That link shows more variables than I have (I think) like lambda values, etc.

 

[8point1]

Please, any help would be appreciated. I'm not looking for an answer, just a push in the right direction. Here's what I've tried to do to start out:

-put integral in terms of V
-break down Volume values and try to solve for r and h
-ratio between starting values: 100lb/in^2 and 400in^3

?

 

[SteamKing]

The attached article shows how to integrate P dV when PV^gamma = k (Note: there are no lambdas present.) Work is explicitly given in terms of initial pressure and initial and final volumes. (See section "Derivation of discrete formula")