Question

the volume V of a gas at a constant temperature varies inversely with the pressure P. when the volume is 100 cubic inches the pressure is 25 pounds per square inch. what is the pressure when the volume is 125 cubic inches ​

Answer 1

The pressure is
`20\ psi`

Explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

In this problem we have

`V*P=k`

where

V is the volume of a gas at a constant temperature

P is the pressure

we have

For
`V=100\ in^(3)`,
`P=25\ psi`

step 1

Find the value of k

substitute the values of V and P

`100*25=k`

`k=2,500`

The equation is equal to
`V*P=2,500`

step 2

Find the pressure when the volume is 125 cubic inches

For
`V=125\ in^(3)`

substitute in the equation and solve for P

`125*P=2,500`

`P=2,500/125=20\ psi`