Question

The volume of a gas in a container varies inversely with the pressure on the gas. A container of argon has a volume of 336in3 under a pressure of 2,500psi (pounds per square inch).

Write the equation that relates the volume, V, to the pressure, P.

What would be the volume of this gas if the pressure is decreased to 2,000psi?

Answer 1

V=840,000/P 420 cubic inches

Explanation:

We are given that the volume, V, of a gas is inversely proportional to to the pressure, P, in the container. So V=k/P for some constant, k. To determine the value of k, substitute the known values, V=336 when P=2,500, to find that

336=k/2,500

Multiplying by 2,500 gives k=840,000, so an equation that relates V and P is

V=840,000/P

Substituting P=2,000 gives

840,000/2,000=420

So under a pressure of 2,000psi, the gas has a volume of 420in3.

Answer 2

420 in3

Explanation:

let V represent volume and P pressure hence the equation is

V∝
`\frac {1}{P}`

Relating this with a constant k

`V=\frac {1}{kP}`

We can then say that
`VP=\frac {1}{k}`

Considering that when volume and pressure change then we can write

`V1P1=V2P2=\frac {1}{k}`

Therefore, the equation that relates volume to pressure is
`V=\frac {1}{kP}` where k is constant

Considering that
`V1P1=V2P2=\frac {1}{k}`, let volume of 336 in3 be V1, pressure of 2,500 psi be P1, pressure of 2,000 psi be P2 and making V2 the subject of our formula

`V2=\frac {V1P1}{P2}=\frac {1}{k}`

`V2=\frac {336*2500}{2000}=420 in3`

Therefore, the pressure increases to 420 in3