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?
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?
Comments
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
Answer:
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