Question

An enclosed gas exerts a pressure P on the walls of a container. This pressure is directly proportional to the temperature T of the gas, measured in Kelvin. If the pressure is 7 lb per square inch when the temperature is 420ºK, find the constant of variation.

Answer 1

Don't know if i'm right but I got 1/60

Answer 2

Keywords:

Variation constant, directly proportional, temperature, pressure

For this case, we must find the constant of variation, knowing that the pressure is directly proportional to the temperature, knowing the values of pressure and temperature. So, we have:

`P = aK`

Where "a" is the constant of variation or constant of proportionality

If
`P = 7 \frac {lb} {in ^ 2}\\T = 420K`

Substituting:

`7 \frac {lb} {in ^ 2} = a*420K`

Clearing to:

`a = \frac {7} {420} \frac {lb} {K * in ^ 2}`, if we divide by 7 the numerator and denominator we have:

Thus, the constant of variation is given by:

`a = \frac {1} {60} \frac {lb} {K * in ^ 2}`

Answer:

The variation constant is given by:
`a = \frac {1} {60} \frac {lb} {K * in ^ 2}`