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!

 

[TSny]

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.

Was this what you were thinking?

 

[TSny]

Yes. But there's no need to find P₃. You can use P₂ and V₂ instead of P₃ and V₃.