Help with Thermodynamics and Gas Law

[sonpat]

THE PROBLEM:
A steam engine's boiler completely converts 2638 g of water at 83.7 °C to steam at 195.4 °C. The steam, at a constant pressure of 3.28 Pa, expands by pushing a piston of radius 9.4 cm a distance of 8.3 cm. What is the change in internal energy of the water-steam system? MY WORK:
First I know Change In Internal Energy = Heat - Work
So I found heat using MC Delta T and Heat of Vaporization. I got 6665124.107 J.
Then I found work.
Change in Volume = Area * Distance
So in this case it's Pi R2 D or (.094m2)(pi)(.083m) which is .002304m3
Then Work = Change in Volume * Pressure
3.8 pascals* .002304m3 = .008755 J
Change in internal energy = 6665124.107 J - .008755 J = 6665124.098J

BUT THAT'S WRONG AND I DON'T KNOW WHAT I AM DOING

 

[Chestermiller]

Something seems very unusual about this problem statement. Is this the exact wording. That 3.28 Pa is very suspect.

Are you supposed to be using the steam tables for this?

 

[sonpat]

Something seems very unusual about this problem statement. Is this the exact wording. That 3.28 Pa is very suspect.

Are you supposed to be using the steam tables for this?

yes this is the exact wording and I believe so

 

[Chestermiller]

Sorry. I'm not able to make sense out of the problem statement. Maybe someone else can figure it out.

 

[SteamKing]

THE PROBLEM:
A steam engine's boiler completely converts 2638 g of water at 83.7 °C to steam at 195.4 °C. The steam, at a constant pressure of 3.28 Pa, expands by pushing a piston of radius 9.4 cm a distance of 8.3 cm. What is the change in internal energy of the water-steam system? MY WORK:
First I know Change In Internal Energy = Heat - Work
So I found heat using MC Delta T and Heat of Vaporization. I got 6665124.107 J.
Then I found work.
Change in Volume = Area * Distance
So in this case it's Pi R2 D or (.094m2)(pi)(.083m) which is .002304m3
Then Work = Change in Volume * Pressure
3.8 pascals* .002304m3 = .008755 J
Change in internal energy = 6665124.107 J - .008755 J = 6665124.098J

BUT THAT'S WRONG AND I DON'T KNOW WHAT I AM DOING

A pressure of 3.28 Pa absolute is a pretty strong vacuum, and even a gauge pressure of 3.28 Pa is essentially atmospheric. From a practical standpoint, this figure is in error.
A pressure of 1 Pa is created by a dollar bill resting on a flat surface. Atmospheric pressure is 101,325 Pa.

When you say you found the heat added to the water by using MC delta T and Heat of Vaporization, how did you calculate the heat added to the steam after it has supposedly been turned to vapor? This is where steam tables come in handy, but only if you know the pressure.