The volume of a balloon (V) and the pressure on that balloon (P) are related by the equation: PV=4500 (Boyle's Law). At a particular moment in time, the pressure on the balloon is 20 psi (pounds per square inch) and is increasing at the rate of 2.4 psi/hour. At what rate is the volume (measured in in^3) changing at that time? Label your answer with the appropriate units)

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Asked Nov 15, 2019
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The volume of a balloon (V) and the pressure on that balloon (P) are related by the equation: PV=4500 (Boyle's Law). At a particular moment in time, the pressure on the balloon is 20 psi (pounds per square inch) and is increasing at the rate of 2.4 psi/hour. At what rate is the volume (measured in in^3) changing at that time? Label your answer with the appropriate units)

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Expert Answer

Step 1
At a particular moment in time, the pressure on the balloonis 20 psi. The PV
relationship equation is given as Pv = 4500. Thus, the volume at that time
= 4500 /20 =225 inch3.
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At a particular moment in time, the pressure on the balloonis 20 psi. The PV relationship equation is given as Pv = 4500. Thus, the volume at that time = 4500 /20 =225 inch3.

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Step 2
So after one hour the pressure will be (20 2.4) psi 22.4 psi as the
pressure is increasing at the rate of 2.4 psi/hr. So the volume will be
4500 / 22.4 200.89 inch3.
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So after one hour the pressure will be (20 2.4) psi 22.4 psi as the pressure is increasing at the rate of 2.4 psi/hr. So the volume will be 4500 / 22.4 200.89 inch3.

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