# PV diagram-calculating work

1. Feb 15, 2009

### M_CG

1. The problem statement, all variables and given/known data
http://i41.tinypic.com/r7rq5w.jpg
The question is stated in the picture but I'll restate it:
A gas expands from I to F in the figure. The energy added to the gas by heat is 449 J when the gas goes from I to F along the diagonal path. What is the change in internal energy of the gas? Answer i units of J.

2. Relevant equations
(delta)U=Q+W (In this case W is negative because the gas is doing work on the system)
W=P(delta)V

3. The attempt at a solution
Since Q is given, I need to find W done by the gas.
Pressure is not constant, but its change is constant so I can use Paverage
Paverage=2*1.013*105Pa
Therefore W=(2*1.013*105)*2.5L=506,500 Joules
Inputting that into the equation for (delta)U:
449 J-506,500 J= -506,051 J

However this answer was incorrect. I also tried calculating work by finding the area under the graph IF, but this was wrong as well. I'm not really sure what I'm doing wrong. Could someone point me in the right direction?

2. Feb 15, 2009

### davieddy

To get work in Joules (=Nm), you want volume in m^3 not litres, and P in Pa (=N/m^2).

An interesting follow up question would be "how many atoms in each molecule of the gas?"

Last edited: Feb 15, 2009
3. Feb 15, 2009

### M_CG

Thank you! I had a feeling there was something funny going on with my units. I also figured out that I was calculating average pressure incorrectly.
W=(2.25*1.013*105 pa)(.0025m3)=569.8125 J
$$\Delta$$U=449 J-569.8125 J=-120.8125 J

4. Feb 16, 2009