Question

The volume of a gas "V" varies inversely with the pressure "P" put on it. If the volume is 360cm³ under a pressure of 20 kgcm2

, then what pressure is needed for it to have a volume of 480cm³?

Answer 1

If two variables vary inversely, then their product is constant:

`x=(k)/(y)\implies xy=k`

So, since
`(V,P)=(360,20)` is a valid couple, we know that for each other couple we must have

`VP=360\cdot 20 = 7200`

So, given the new value for the volume, we have

`480P=7200\iff P=(7200)/(480)=150`

Answer 2

15 Kg cm²

Explanation:

Given that V varies inversely with P then the equation relating them is

V =
`(k)/(P)` ← k is the constant of variation

To find k use the condition

V = 360, P = 20, then

360 =
`(k)/(20)` ( multiply both sides by 20 )

k = 7200

V =
`(7200)/(P)` ← equation of variation

When V = 480, then

480 =
`(7200)/(P)` ( multiply both sides by P )

480P = 7200 ( divide both sides by 480 )

P = 15