Boyle's Law states that when a sample of gas iscompressed at a constant temperature, the pressure P and volume Vsatisfy the equation PV = C, where C is a constant. Suppose that ata certain instant the volume is 900 cm3 , the pressure is 160 kPa,and the pressure is increasing at a rate of 40 kPa/min. At whatrate is the volume decreasing at this instant?
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Step 1: Write all the rates in the problem (including the one youare trying to find) as
derivatives.
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Step 2: Identify the dependent variables in the derivatives. Findan equation relating
the dependent variables in the derivatives. You will often need aformula from
geometry for this.
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Step 3: Differentiate both sides of the equation from Step 2 withrespect to the
independent variable time. The result will be an equation relatingthe rates (relating the
derivatives).
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Step 4: Substitute the values that you are given in the problem forthe derivatives and
the variables and solve for the derivative for which the questionis asking.
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Thanks for any help!!!
