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| Math Central | Quandaries & Queries |
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Question from leria, a student: In Boyle's law, the pressure of gas varies inversely with the volume of the gas. A volume of 11.2 liters of air exerts a pressure of 2.0 atmospheres. determine the constant of variation and write an equation the models the relationship between the pressure of the gas P and its volume, V. Use the equation to predict the volume of air necessary to exert a pressure of 0.25 atmospheres. I wanted to use a ration to solve this problem. 11.2 / 2.0 = x / 0.25 2X = 2.8 2.8 / 2 = 1.4 Will it take 1.4 volume of air to exert a pressure of 0.25. I know you like for the students to try to solve it. However I'm not sure if I'm on the correct track. Please help. Thank you. |
Hi Leria,
You are a little off track. Boyle's Law does say that the pressure of gas varies inversely with the volume of the gas. This means as one increases the other decreases. The formula you need is as follows:
Pressure1 × Volume1 = Pressure2 × Volume2
To find a constant variation use
PV = k
where:
P denotes the pressure of the system.
V is the volume of the gas.
k is a constant value representative of the pressure and volume of the
system.
Think of k as being the same as the slope of your equation.
Janice
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