Question

If the pressure on a gas sample is tripled and the absolute temperature is quadrupled, by what factor will the volume of the sample change?

Answer 1

Let as assume the simplest calculation by assuming that the gas is ideal. Therefore, the equation would be PV=nRT, where P is pressure, V is volume, n is the amount of moles of gas, R is the gas constant and T is the absolute pressure. Let us further assume that the amount of gas, n, is constant before and after the change. With that being said, the volume is equal to

V = nRT/P = kT/P

The term k is lumped as a constant because they are the same before and after the change. Next, we find the ratio of V1 (before the change) and V2 (after the change).

V2/V1 = (k*4T/3P)/(kT/P)

Cancelling out like terms would yield

V2/V1 = 4/3

Therefore, the volume after the change is 4/3 of the original volume. This means that the volume increased by (4/3-1 = 1/3 or 33%) 33% after the change of conditions.