Expert: Paul Klarreich - 10/20/2005

Question
The pressure P os a sample of gas is directly proportional to the temperature T and inversely proportional to the volume V.

what is the equation that expresses this variation?

Find the constant of proportioanlity if 100 L of gas exeerts a presure of 33.2kPa at a temperature of 400 K (absolute temperature measured on the Kelvin scale).

And if the temperature is increased to 500 K and the volume is decreased to 80 L, what is the pressure of the gas?

Answer
Hi, Jennifer,

"P is directly proportional to T" is generally expressed as:

P = k1 T, where k1 is some constant.

"P is inversely proportional to V" is generally expressed as:

P = k2/V, where k is some constant.

When you have both at once, you write:

P = kT/V, where the k is a 'combination' of the k1 and k2 above.  (You only need one k.)

So you just set  V = 100, P = 33.2.  T = 400  and solve for 'k'.

100 = k(400)/33.2


After that, take the answer (the value of k) and substitute it back, using T = 500, V = 80, to solve for P.