Why is the equation for compression work P=kV and not P=Pi/Vi?

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Homework Statement


I am doing a problem of compression work. in order to solve it, I have to find an equation for the line and integrate it to get the work. But I don't understand why ##k = \frac{P_i}{V_i}##

Homework Equations



P=kV

The Attempt at a Solution



Why is it Pi / Vi and not Pf / Vf ? They both give different answers. In original units of atmospheres and liters they both give the same number (1). IT is when you convert to meters cubed and N/meters cubed that the value of k is different. it is not far off, but slightly.

Is it just a margin of error, but in general either one works. Or is using the initial values a matter of importance.
 
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There are different ways of calculating compression work depending on what happens to the heat generated by the compression process .

There are sometimes practical things to take into account as well such as effect of dead volume .

Can you tell us more exactly what problem you are working on ?