What is the Efficiency of a Gas Machine in an A->B->C Change?

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Homework Help Overview

The discussion revolves around determining the heat transfer (Q) for a gas undergoing a change from state A to B to C, as well as assessing the efficiency of the gas machine involved in this process.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using the work formula W=pV and the ideal gas law PV=nRT to derive relationships between pressure, volume, and temperature changes. There are attempts to express changes in temperature (dT) and work done (W) during the transitions, but questions arise about how to calculate heat transfer (Q) from these equations.

Discussion Status

The discussion is ongoing, with participants exploring various equations and relationships. Some guidance is offered regarding the use of the internal energy equation \DeltaU = \DeltaQ + \DeltaW, but no consensus or clear resolution has been reached regarding the calculation of Q or the overall usefulness of the machine.

Contextual Notes

Participants note the need for additional information, such as the number of moles of gas and the gas constant R, as well as temperature values at specific points, to fully address the problem.

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Homework Statement



The task is to get Q, that gas has received through A-B-C change?
Second task is to get usefulness of the machine?

http://img40.imageshack.us/img40/8372/toplinaabc.jpg

Homework Equations



W=pV

The Attempt at a Solution



If I use W=pV i get 0 from A->B so i can't get usefulness. No idea.
 
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To get the heat energy in or out of system one requires the value of the number of moles of gas and the gas constant R or the temperatures at some points on the graph.
 
So from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR?

from B->C formula is W=p2(v2*v1) and with ideal gas dT=(p2(v2-v1))/nR?

But how to get Q from that?
 
the_man said:
So from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR?

from B->C formula is W=p2(v2*v1) and with ideal gas dT=(p2(v2-v1))/nR?

But how to get Q from that?

from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR ...yes

from B->C formula is W=p2(v2*v1) ...replace * by -

dT=(p2(v2-v1))/nR ...yes

To get the heat transfer one can use \DeltaU = \DeltaQ + \DeltaW where U is the internal energy.
 
okay man, thanks!
 

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