I'm confused about mathematical expression concerning Boyle's Law. Can you help me out?

Asked by Blackberry (34121

) January 17th, 2012

I’m refreshing my physics and came in contact with a symbol I haven’t seen before.

For Boyle’s law, it can be written a few ways.

In the book I’m using, which is a navy publication, it simplified Boyle’s Law as VP=V’P’

I wasn’t sure what the ’ was, so I looked it up and it said:

“In physics, the prime is used to denote variables after an event. For example, VA′ would indicate the velocity of object A after an event.”

But I’m still not grasping the concept.

Here’s an example of Boyle’s Law from the book:

V= initial volume
P= inital pressure
V’= new volume
P’= new pressure

20cm3 of gas a has a pressure of 1,000 hPa. The pressure is increased to 1,015 hPa. What is the new volume?

So, 20 x P = V’ x P’

20×1000 = V’ x 1015

20,000 = V’ x 1015

So V’ = 20,000/1015 which is 19.70cm3

My question is: where did the division come from? I get the rest, and the division makes sense, but I don’t understand why I’m supposed to divide. Does it have something to do with the prime (’)?

Other examples show Boyle’s Law as pV=k and P1V1 = P2V2

And why is it pressure to volume for one and volume to pressure on another?

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3 Answers

VP = V’P’
means the same as
V1P1 = V2P2

In other words, the product of V and P remains the same after any change in volume or pressure, provided everything else stays the same.

Don’t confuse the prime symbol here with its unrelated use to denote the derivative of a function, which is not the intended meaning in this context.

gasman (11345

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I might not be understanding your question correctly so this might not help, but this is how I think of it: What Boyle’s law is trying to tell you is that volume times pressure will always be equal to volume times pressure. So if you change either one, you will need to change the other one to make the expression stay equal.

In your example, the initial volume x pressure was (20) x (1,000) = 20,000. After some change, pressure increases. So do you expect volume to increase or decrease?

In order for volume x pressure to remain equal to what it was in the first place (20,000), if pressure increases, volume has to decrease. And in order to calculate how much it has to decrease, just solve the expression for V’.

Does that make sense?

nikipedia (28095

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@gasman Ah ok, gotcha :D

@nikipedia Yeah, I think I got it :D

Thanks a lot.

Blackberry (34121

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