PV diagrams for ideal gas: Finding Work Done

AI Thread Summary
The discussion revolves around calculating the work done by an ideal gas represented on a PV diagram, specifically from point A (300 kPa, 0.5 L) to point B (500 kPa, 1 L). The initial calculation of work as 100 J is questioned, as the textbook states it should be 200 J. Participants emphasize that the area under the graph must account for the true zero pressure, suggesting the use of trapezoidal area calculations. Clarifications are made regarding the correct geometric shape for the area calculation, confirming it should be a trapezoid. Accurate area calculation is essential to determine the correct work done by the gas.
slaw155
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Homework Statement


Imagine a graph of pressure in kPa (y-axis) against volume in L (x-axis). There is a straight line moving from point A at 300kPa, 0.5L to point B at 500kPa, 1L. The false origin on this graph is 200kPa, 0L. What is the work done by the gas?


Homework Equations



W=pV

The Attempt at a Solution


I know that work is area under graph so its basically the area of a triangle plus area of trapezium. But this gives work = 100J but textbook says 200J. Where have I gone wrong?
 
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See the picture . You need the blue area from the really zero pressure.

ehild
 

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slaw155 said:

Homework Statement


Imagine a graph of pressure in kPa (y-axis) against volume in L (x-axis). There is a straight line moving from point A at 300kPa, 0.5L to point B at 500kPa, 1L. The false origin on this graph is 200kPa, 0L. What is the work done by the gas?

Homework Equations



W=pV

The Attempt at a Solution


I know that work is area under graph so its basically the area of a triangle plus area of trapezium. But this gives work = 100J but textbook says 200J. Where have I gone wrong?
Use the formula for area of a trapezoid: (L1 + L2)/2 x W

AM
 
Last edited:
Andrew Mason said:
Use the formula for area of a parallelogram: (L1 + L2)/2 x W

AM

You meant trapezoid, I think :smile:

ehild
 
ehild said:
You meant trapezoid, I think :smile:

ehild
Right. A trapezoid.

AM
 

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