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

Answer:

Step-by-step 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,

$k=\frac{3}{220}$

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.

$P=(\frac{3}{220})380$ so

P = 5.181818 or as an equivalent fraction,

$P=\frac{513}{100}$