Variation Pressure and Volume

Question

The pressure of a gas varies inversely as the volume. If the pressure is 40 psi when the volume is 10 cubic meters, what will the pressure be when the volume is 16 cubic meters?

Answer 1

Hi there! I'd love to help you with this :)

Inverse variation is written as follows:

y = k / x Where k is a constant, y is our pressure, and x is our volume.

We first need to find the constant. To find k, we will plug 40 in for y and 10 in for x and then solve for our constant:

40 = k / 10

40 * 10 = k

400 = k

Now we have the equation:

y = 400 / x

Now plug 16 in for x and solve again:

y = 400 / 16

y = 25

I hope this explanation was thorough and answered all of your questions! If you have additional questions don't hesitate to reach out. Learn on! :)

Answer 2

It is useful to think about the meaning of "varies inversely as"---or sometimes "inversely proportional to":

If 2 parameters have this kind of relationship, it means that--if one is reduced by a stated factor--the other is increased by the same factor.

In this case, we are given the ratio between 2 values--multiply #1 by x to get #2.

To apply the inverse proportion, we divide by x

Answer 3

pv= k

(40)(10) = k

400 = k

p(16) = 400

p = 25