The volume of a gas varies inversely as applied pressure if the pressure acting on a 45m^3 of gas is lowered from 3 atmospheres to 2 atmospheres what new volume does the gas occupy
if p = 3, v = 45
if p = 2 , v = x
3/2 = x/45
2x = 135
x = 67.5
or
V = k(1/p)
for x = 3, v = 45
45 = k/3
k = 135
then V = 135/p
when p = 2
V = 135/2 = 67.5
To find the new volume of the gas, we can use the inverse variation formula:
Volume 1 * Pressure 1 = Volume 2 * Pressure 2
Let's plug in the given values:
45m^3 * 3 atm = Volume 2 * 2 atm
Now, let's solve for Volume 2 by rearranging the equation:
Volume 2 = (45m^3 * 3 atm) / 2 atm
Canceling out atm (atmospheres) and calculating:
Volume 2 = (45m^3 * 3) / 2
= 135m^3 / 2
= 67.5m^3
Therefore, the gas now occupies a volume of 67.5m^3.