Question

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a 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 what rate is the volume decreasing at this instant?

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Step 1: Write all the rates in the problem (including the one you are trying to find) as
derivatives.

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Step 2: Identify the dependent variables in the derivatives. Find an equation relating
the dependent variables in the derivatives. You will often need a formula from
geometry for this.

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Step 3: Differentiate both sides of the equation from Step 2 with respect to the
independent variable time. The result will be an equation relating the rates (relating the
derivatives).

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Step 4: Substitute the values that you are given in the problem for the derivatives and
the variables and solve for the derivative for which the question is asking.

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Thanks for any help!!!

Answer 1