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.
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?