# Math word problem?

Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 5 L, the pressure is 212 kPa (kilopascals). What is the volume when the pressure is 530 kPa?

Relevance

Let V be the volume (in liters)

Let P be the pressure (in kilopascals)

If they varied *directly* then we would say that the volume (V) was equal to a constant (k) *times* the pressure (P).

But they vary *inversely*. So the volume (V) is equal to a constant (k) *divided* by the pressure (P):

V = k/P

Plug in your first data point (V = 5, P = 212) and figure out k:

5 = k/212

k = 5 * 212

k = 1060

Now you have a complete equation:

V = 1060/P

Plug in your new pressure to figure out the new volume:

V = 1060/530

V = 2

2 liters

P.S. The shortcut equation would be

5 * 212 = 530 * P

1060 = 530P

P = 2

• Okay, if volume varies inversely with pressure, then we have an equation V = k/P where k is some constant that will make the equation true

We know that when V=5, P=212

5 = k/212

5(212) = k

1060 = k

Now that we know k, we can use it to find any V

V = 1060/P

V = 1060/530

V = 2

the volume is 2 L when the pressure is 530 kPa

• P1.V1 = P2.V2

P1.V1 = 212 * 5 = 1060

P2.V2 = 530 * V2 = 1060

V2 = 1060/530 = 2L