There's a problem in my thermo class that I think I have the right answer for, but the value I get doesn't seem to make sense. The problem reads:(adsbygoogle = window.adsbygoogle || []).push({});

Warm air is contained in a piston-cyliner assembly oriented horizontally. The air cools slowly from an intial volume of .003 m^3 to a final volume of .002m^3. During the process, a spring exerts a force that varies linearly from an intial value of 900N to a final value of zero. The atmospheric pressure is 100kPa, and the area of the piston face is .018m^2. Friction between the piston and the cylinder wall can be neglected. For the air, determine the intial and final pressures, in kPa, and the work in kJ.

So I split the system up into two states.

State 1: V1 = .003 m^3 Fspring = 900N

State 2: v2 = .002 m^3 Fspring = 0N

I found the pressures for each state using a force balance equation and the relationship between force and pressure.

I came up with:

Fair = Fspring + Farm

(Pair)(Apiston) = Fspring + (Pair)(Apiston)

Using the values for State 1 and 2 I came up with 150 kPa for State 1 and 100 kPa for state 2.

Here's where I run into problems. Calculating the work.

First off I make the assumption that the magnitude of the work done as the spring moves is equal to the magnitude of the work the air does during this change.

Therefore, I used 1/2kx^2 for work done. I found the distance the spring moved using (V2-V1)/Apiston = delta X

Using this x value I went to Fspring = 900 = kx and found k.

From here I used evaluated 1/2kx^2 and I came up with an answer of 25Joules.

My question is, is the answer I getting make sense physically, because it seems like a really small answer, also are the assumptions I am making for work done correct, or is there another way I should go about this.

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# Homework Help: Work done as air expands in piston with spring

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