Question

The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. If the pressure is 6 pounds per inch when the temperature is 440 F, find the pressure exerted when the temperature of the gas is 380 F?

Answer 1

Explanation:

If y is directly proportional to x, then the formula for that is a linear one:

y = kx, where k is the constant of proportionality. In our situation, if the pressure is directly proportional to the temp, then our formula is

P = kT. We need to find that value of k. Plug in what we have:

6 = k(440) so

k = .01363636 or as an equivalent fraction,

`k=(3)/(220)`

Now that have that value of k, we can use it in the formula again, this time with a different value for T to solve for P.

`P=((3)/(220))380` so

P = 5.181818 or as an equivalent fraction,

`P=(513)/(100)`