# 1st Law of Thermo, work in a piston.

twmggc

## Homework Statement

Air is expanded in a piston-cylinder arrangement at a constant P of 200kPa from a volume of 0.1 m3 to a volume of 0.3m3. Then the temperature is held constant during an expansion to a volume of 0.5m3. Predict the total work done in the air.

## Homework Equations

W = ∫PdV , PV = nRT

## The Attempt at a Solution

For the first part of the expansion I used:
W = ∫PdV = P∫dV = P(V2 - V1) = 200,000Pa ( 0.3-0.1)m3
and got W = 40,000J.

The next expansion is what is confusing me.
Since Pressure is no longer constant I need to leave it in the W = ∫PdV equation.
So, I transform this equation using the ideal gas eqn. PV = nRT and get:
W = nRT∫dV/V = nRT*ln(V3/V2)
But, without knowing the n or the T how do I get the work?

Thanks!

## The Attempt at a Solution

Homework Helper
Gold Member
Trick: Replace the nRT in your expression for W with some other expression (using the ideal gas law).

twmggc
Since Temperature is constant for this part I can assume P2V2=P3V3 and find P3 and then replace nRT in my work equation with P3V3 (PV = nRT).
After my computations I got 30,649.54J which sounds within reason.