Inverse Proportion: By what % will gas press. change if vol. incr. by 25%?

[Sharon3431]

Hi Everyone
This is the first time I have posted. Hope that all you clever people out there can help me:

At a constant temperature, the volume of gas V is inversely proportional to it's pressure p.
By what percentage will the pressure of a gas change if it's volume increases by 25%?

Have got s far as V= K/P......don't know how to proceed.
Thanks

 

[stapel]

At a constant temperature, the volume of gas V is inversely proportional to its pressure P.
By what percentage will the pressure of a gas change if it's volume increases by 25%?

I have gotten as far as [my variation equation,] V= k/P......but I don't know how to proceed from there.

One way to proceed might be to plug the given information into the formula. You are told that the original volume V is now 1.25V. You are asked to find the new pressure P. So plug this in:

. . .original:

. . . . .V = k/P so P = k/V and k = PV

. . .new:

. . . . .(new V) = 1.25(old V) = 1.25V

. . . . .1.25V = (PV)/(new P)

. . . . .(1.25V)/V = P/(new P)

Do the cancellation on the left. (Nothing cancels on the right, of course.) Solve for "new P =" to see how the new pressure relates to the original pressure.

 

[Sharon3431]

One way to proceed might be to plug the given information into the formula. You are told that the original volume V is now 1.25V. You are asked to find the new pressure P. So plug this in:

. . .original:

. . . . .V = k/P so P = k/V and k = PV

. . .new:

. . . . .(new V) = 1.25(old V) = 1.25V

. . . . .1.25V = (PV)/(new P)

. . . . .(1.25V)/V = P/(new P)

Do the cancellation on the left. (Nothing cancels on the right, of course.) Solve for "new P =" to see how the new pressure relates to the original pressure.

Thank you very much. I see that I had to write K in terms of P and V, and then rearrange. So then I got
(New p) = P/1.25. Is it right for me to put 1 as the value for P, in which case the answer is 0.8 which means it has dropped by 20%. However, if I'm honest I'm not entirely sure why P = 1?

 

[Sharon3431]

Inverse proportion

Thank you very much Stapel! I see now my first step should have been to write k in terms of p and v. I can follow through to get ( new p) = P/1.25. I think I should now be substituting P = 1 in which case I get 0.8 which means the change in pressure is 20%...........but if I'm really honest I'm not sure why P is 1? I really like the fact that you helped to guide me to the answer. Apologies if you have another reply, but as I am new to the site I am not sure how answering a thread is different to answering with a quote, so I did both.

 

[stapel]

Thank you very much Stapel! I see now my first step should have been to write k in terms of p and v.

When in doubt of what you definitely should do, try fiddling with what you know you can do. At first glance, I wasn't sure how to proceed. But then I tried solving the one equation, and then doing some substitution. And happy things occurred.

I can follow through to get ( new p) = P/1.25.

Showing your steps, we get something along the lines of:

. . . . .(1.25 V)/V = P/(new P)

. . . . .1.25 = P/(new P)

. . . . .1.25 (new P) = P

. . . . .(new P) = P/1.25 = P/(5/4) = (4/5)P = 0.8P

...so the new pressure is [what percentage?] of the old pressure.

I think I should now be substituting P = 1...

Why? By what mathematical logic?

 

[Sharon3431]

Inverse proportion

Oh yes! Thanks. Got totally confused with this. Doesn't matter if P is 234 or 1.265, we are now only getting 4/5 or 80% of it. This is a great forum and you have helped me enormously!