Physics Help Forum pV is a constant

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 Sep 4th 2008, 07:55 AM #1 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 pV is a constant For a graph with pV against p, it should be a straight horizontal line. However, regarding the slope, slope equals=V = 0 , isn't that ridiculous?
Sep 4th 2008, 08:33 AM   #2

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 Originally Posted by werehk For a graph with pV against p, it should be a straight horizontal line. However, regarding the slope, slope equals=V = 0 , isn't that ridiculous?
The slope of a horizontal line is 0. You are saying that the slope should equal V which is 0, or is this a typo?

The relationship expressed by a p vs. V plot can, in general, be complicated. For an ideal gas we easily have that the pressure is inversely proportional to the volume, so the graph is a curve. However for different physical systems we can typically arrange the system to have a variety of different behaviors, on of which is that the pressure is independent of the volume, ie. the slope of the p vs. V graph is 0.

-Dan
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Sep 4th 2008, 09:05 PM   #3
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 Originally Posted by topsquark The slope of a horizontal line is 0. You are saying that the slope should equal V which is 0, or is this a typo? The relationship expressed by a p vs. V plot can, in general, be complicated. For an ideal gas we easily have that the pressure is inversely proportional to the volume, so the graph is a curve. However for different physical systems we can typically arrange the system to have a variety of different behaviors, on of which is that the pressure is independent of the volume, ie. the slope of the p vs. V graph is 0. -Dan
Ya, I'm saying that volume equals the slope which is zero.

So does it mean that there is no special meaning for the slope and we can't use the slope for interpretation and analysis of other variables?

Last edited by werehk; Sep 4th 2008 at 09:08 PM.

Sep 5th 2008, 09:41 AM   #4

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 Originally Posted by werehk Ya, I'm saying that volume equals the slope which is zero. So does it mean that there is no special meaning for the slope and we can't use the slope for interpretation and analysis of other variables?
Well, if the volume is equal to zero then we DO have a serious problem, as the object can only be a black hole! My guess is that something was not labeled correctly on the diagram.

As far as the slope of th curve being zero this means that the process taking the system from one point to another on the curve is "isobaric" (constant pressure.) This determines how many of the different properties of the system relate to each other, thermodynamically speaking, so it is a very important piece of information. More than that I cannot say because my Thermodynamics is awfully rusty.

-Dan
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 Oct 11th 2008, 09:35 PM #5 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 Would it be more appropriate to say that for pV/P, the P is the applied pressure rather than the gas pressure? As I found it would be more appropriate for explanation.

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