Calculate the work done by an ideal gas.

[miamirulz29]

Homework Statement

1 mole of an ideal gas is at 7 atm pressure, occupies 6L and has an internal energy of 508 J. the gas is first cooled at constant volume until its pressure is 1 atm. It is then allowed to expand at constant pressure until its volume is 8L with an internal energy of 814 J. Calculate the work done by the gas. Answer in units of J.

Homework Equations

Work = P * DeltaV
PV = nRT
Work = nRT

The Attempt at a Solution

I tried doing the last equation, but I do not know the temperature. For P*V, which P do I use, the 7atm or 1 atm? I know I have to convert to Pa and the m^3.

 

[Fightfish]

A simple way to start the question would be to draw a P-V diagram. The work done by the gas/on the gas is simply the area underneath the graph depicting the changes (after adjusting for the appropriate sign).
Otherwise, you should break up the process into two parts: the isochoric (constant volume) and the isobaric (constant pressure) processes. Then, compute the work done by/on the gas for each part.

By the way, $$P \Delta V$$ is definitely not equal to PV! The work done by the gas in an infinitesimal step is equal to the pressure multiplied by the change in volume. The equation $$Work = P \Delta V$$ is true only for constant pressure; for general cases, we have to employ the integral $$Work = \int P dV$$ with the appropriate boundaries.