SOLUTION: The volume (V) of a gas varies inversely as the pressure (P) on the gas. If the volume of a gas is 12 ft3 when the pressure is 13 lb/ft2, find the volume of the gas when the pressu

Question 1197039: The volume (V) of a gas varies inversely as the pressure (P) on the gas. If the volume of a gas is 12 ft3 when the pressure is 13 lb/ft2, find the volume of the gas when the pressure is 4 lb/ft2.
v=__________?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Boyle's law states that for a fixed mass of gas at constant temperature, the absolute pressure and the volume of a gas are inversely proportional.

given:

then

answer:

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The work in the response from the other tutor is very hard to follow, largely because she keeps units in all her calculations and displays them poorly. In the end a mysterious factor of 8 appears which makes her answer incorrect -- a fact she could easily have seen if she had checked her answer.

In fact all you need to do to solve the problem is use her initial equation and fill in the numbers:

ANSWER: 39 cubic feet

I personally would not even have used the fact that the product of the volume and pressure is a constant. The information is not given that way; and solving the problem using the inverse variation fact is far easier.

Between the two scenarios, the pressure changes by a factor of 4/13; the inverse variation says the volume changes by a factor of 13/4:

ANSWER: 39

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