Help with Thermodynamics and Gas Law

AI Thread Summary
The discussion revolves around calculating the change in internal energy for a steam engine's water-steam system, given specific parameters. The user calculated heat using the formula MC Delta T and the heat of vaporization, arriving at 6,665,124.107 J, but found the work done to be only 0.008755 J due to an unusually low pressure of 3.28 Pa. Concerns were raised about the validity of this pressure, as it is significantly lower than atmospheric pressure and suggests a vacuum scenario. Additionally, the need for steam tables was highlighted to accurately determine the heat added to the steam after vaporization, emphasizing the importance of knowing the pressure for correct calculations. The overall consensus is that the problem statement may contain errors, particularly regarding the pressure value.
sonpat
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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
 
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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?
 
Chestermiller said:
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
 
Sorry. I'm not able to make sense out of the problem statement. Maybe someone else can figure it out.
 
sonpat said:
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.
 
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