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## Homework Statement

Air occupies [itex]0.140m^3[/itex] while under gauge pressure of [itex]1.03x10^5[/itex]

It is then expanded isothermically to atmospheric pressure.

Then it is cooled at constant preesure back to its initial volume.

And then I should calculate the work done by the gas.

## Homework Equations

[itex] W=(nRT) \ln \frac{v_{1}}{v_{2}} [/itex]

[itex] PV=nRT [/itex]

## The Attempt at a Solution

First I need to know how many mols of air I have.

So I convert [itex] 0.140 m^3 [/itex] to centimeters and since 1 mol of anything occupies [itex]22.4 L [/itex] or [itex]22400 cm^3[/itex] I find that I have 6.25mols of air.

Then I find the initial temperature of the system using [itex] T_{i} = \frac{PV}{Rn} = 277.6K [/itex]

And then I'm stuck here

I tried before calculating the final volume and with this the ln between initial and final volumes.

but I made the wrong assumption that temperature was constant which is not true.

Now I'm stuck because I'm not sure how to calculate the final volume.