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

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SUMMARY

The equation for compression work is defined as P = kV, where k is determined by the initial pressure (P_i) and initial volume (V_i) of the gas. The distinction between using initial (P_i, V_i) versus final (P_f, V_f) values is crucial, as it affects the accuracy of the calculated work due to differences in units and conversion factors. The discussion highlights that while both approaches yield similar results in certain units, using initial values is essential for precise calculations in thermodynamic contexts. Additionally, factors such as heat generation and dead volume must be considered in practical applications.

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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 ?
 

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