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

Answer 1

Answer:

15 Kg cm²

Step-by-step explanation:

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

V = $\frac{k}{P}$ ← k is the constant of variation

To find k use the condition

V = 360, P = 20, then

360 = $\frac{k}{20}$ ( multiply both sides by 20 )

k = 7200

V = $\frac{7200}{P}$ ← equation of variation

When V = 480, then

480 = $\frac{7200}{P}$ ( multiply both sides by P )

480P = 7200 ( divide both sides by 480 )

P = 15

Answer 2

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

$x=\dfrac{k}{y}\implies xy=k$

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

$480P=7200\iff P=\dfrac{7200}{480}=150$