Question

The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p). If the volume of a gas is 24 cubic centimeters when the pressure is 16 pounds, what is the volume under a pressure of 30 pounds?

a) 45 cubic cm b) 20 cubic cm c) 12.8 cubic cm

Answer 1

Answer : C) 12.8 cubic cm

The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p)

If y is inversely proportional to x then
`y=(k)/(x)`

where k is constant of proportionality

v is inversely proportional to p then
`v=(k)/(p)`

the volume of a gas is 24 cubic centimeters when the pressure is 16 pounds

Given : v= 24 and p = 16. We need to find out k

`24=(k)/(16)`

Multiply by 16 on both sides

k = 384

Now we find out the volume under a pressure of 30 pounds

`v=(384)/(30)`

`v=(128)/(10)`= 12.8 cubic cm