Work done by air in piston with temperature change

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Homework Help Overview

The discussion revolves around a thermodynamics problem involving the work done by air in a piston during an expansion process. The scenario includes two pounds of air in a cylinder, expanding against a constant pressure of 200 psia, with an initial volume of 0.5 ft³ and a final temperature of 100°F. Participants are exploring the relationships between pressure, volume, and temperature in the context of the ideal gas law.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to determine the initial temperature using the ideal gas law (PV = mRT) but express uncertainty about the appropriate values for R and cv. There are questions regarding which variables remain constant during the process and how to apply the work equation correctly.

Discussion Status

The discussion is ongoing, with participants providing various insights and suggestions for approaching the problem. Some guidance has been offered regarding the use of the ideal gas equation and the need to ensure proper unit consistency. However, there is no explicit consensus on the method to proceed or the assumptions to be made.

Contextual Notes

Participants note the importance of understanding which parameters are constant and the need to assume equilibrium conditions at the final state. There is also mention of potential confusion regarding the correct values for specific heat and gas constant.

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Homework Statement


Two pounds of air contained in a cylinder expand without friction against a piston. The pressure on the back side of the piston is constant at 200 psia. The air initially occupies a volume of 0.5 ft3. What is the work done by the air in ft-lbf if the expansion continues until the temperature of the air reaches 100 F?

Homework Equations


Q - W = m(uf - ui), which translates to W = m*cv*(Tf - Ti) [Q is 0 because there's no heat transfer]
PV = mRT

The Attempt at a Solution


W = 2 lbm (0.171 Btu/lbm R)(559.67 R - Ti)

The text says the answer is 45300 ft-lbf

Basically I don't really know how to start this all off. I know I need to find the initial temperature which I think means I need to use PV = mRT but I can't find an agreeable R value in my book (also I have no idea if my cv value is correct). Could someone just point me in the right direction?
 
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I don't know that Q-W formula, but I think you'll need the initial temperature and final volume, which you can get from the formula PV = mRT, if you think about which of those letters change and which are constant.
 
vertigo said:
I don't know that Q-W formula, but I think you'll need the initial temperature and final volume, which you can get from the formula PV = mRT, if you think about which of those letters change and which are constant.

The thing is I can't really tell what is going to remain constant when I read the question. I think the pressure remains constant and I know mass does which leaves me with Ti/Vi = Tf/Vf. I've already got Vi and Tf but I don't really know what to do with that.
 
In order to answer this, you must assume that the system comes to rest at state 2 and has achieved equilibrium with its surroundings; ie P2=200psi.
Now we can use the ideal gas equation to solve for v2:
V2=(mRT2)/P2.
Some notes here:
1) watch your units! P is in inches and R is in feet.
2) Use the right R value (85.67)
3) T is absolute.
Once you’ve got v2, then w=P(v2-v1) with P=200 psi.
I know pressure is not constant within the system, but it is outside the system. Think of it as the work done on the environment is the work done by the system.
 
You need to make an assumption
 

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