SOLUTION: The volume occupied by a fixed weight of gas (held at a constant temperature) varies inversely as the pressure placed on it. If a gas occupies a volume of 40 cubic meters under a p

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Question 1057150: The volume occupied by a fixed weight of gas (held at a constant temperature) varies inversely as the pressure placed on it. If a gas occupies a volume of 40 cubic meters under a pressure of 7 atmospheres, find the volume that the gas occupies when the pressure is changed to 6 atmospheres.
Answer by ikleyn(53937) About Me  (Show Source):
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The volume occupied by a fixed weight of gas (held at a constant temperature) varies inversely as the pressure placed on it.
If a gas occupies a volume of 40 cubic meters under a pressure of 7 atmospheres, find the volume that the gas
occupies when the pressure is changed to 6 atmospheres.
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The condition says that the ratio of volumes is inversely proportional to the ratio of pressures.
In math terms, it means that

V%5B1%5D%2FV%5B2%5D = P%5B2%5D%2FP%5B1%5D.

Substitute the given values V%5B1%5D = 40, P%5B1%5D = 7, P%5B2%5D = 6:

40%2FV%5B2%5D = 6%2F7

and find v%5B2%5D from this proportion:

V%5B2%5D = %2840%2A7%29%2F6.

You calculate V%5B2%5D.