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 $y=\frac{k}{x}$

where k is constant of proportionality

v is  inversely proportional to p then $v=\frac{k}{p}$

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

$24=\frac{k}{16}$

Multiply by 16 on both sides

k = 384

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

$v=\frac{384}{30}$

$v=\frac{128}{10}$= 12.8 cubic cm