Homework Help: Ideal gas law mechanical work problem

1. Apr 17, 2013

DrOnline

1. The problem statement, all variables and given/known data

Calculate the gas' mechanical work on its environment for the thermodynamic process path IF.

Solution says: 505 J

2. Relevant equations

W=$$\int_i^f p,dv$$

i = Vi, initial volume
f = Vf, final volume

3. The attempt at a solution

My approach is to find a function for p(v) between 2 and 4 liters.

$$p(v) = 709275 - \frac{3}{2} * 101325 V (Pa)$$

And then integrate it from 2 to 4 liters, which is 0.002m3 to 0.004m3

Problem is, I get:

Which is way off. I should get 505 J..

I'm stumped. What am I doing wrong?

2. Apr 17, 2013

rude man

where did you get your 709275 number?

Anyway, I make it about 306 J.

3. Apr 17, 2013

DrOnline

Oh, I should have stated that. I extended the IF line to where it intersects with the Y-axis, which is 7 atm.

7 * 101325 Pa = 709275 Pa.

You got 306 J... it should be 505, unless the document is wrong.

4. Apr 17, 2013

rude man

The first time I just calculated area = 1/2 bh and got 306.

This time I did the integration and got ~ 518. And I found your mistake - in your 2nd term under the integral you divided by 2 instead of 0.002.

Still don't know why 1/2 bh didn't work!

5. Apr 18, 2013

DrOnline

Thank you for your help. Gonna ask the professor about it, he made the task after all.

The second term is -(3*2) because that is the gradient of the curve. That should be correct.

6. Apr 18, 2013

rude man

It's not correct. The second term should be -(3/2) * 101,325/0.001 V.
I wouldn't go to your professor 'till we agree on this.

7. Apr 18, 2013

DrOnline

My God, that seemed to do the trick.

This seems right to me.

I gather since I converted from atm to Pa, and integrated using m3 instead of liters, I also should have taken that into account for the gradient.

Is that assessment correct?

8. Apr 18, 2013

rude man

That assessment is fully correct!

9. Apr 18, 2013

DrOnline

Thank you very much!