   Chapter 2.8, Problem 37E

Chapter
Section
Textbook Problem

# 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 P V = C , where C is a constant. Suppose that at a certain instant the volume is 600 c m 3 , the pressure is 150 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?

To determine

To find:

The rate at which the volume is decreasing.

Solution:

Volume is decreasing at the rate 80 cm3/min

Explanation

1. Concept:

Using Boyle’s law and differentiation, we can find the rate of change of volume.

2. Formula:

i. Boyle’s Law PV = C, where c is constant.

ii. Product rule of differentiation: ddxfx*gx=fx*ddxgx+gx*ddxfx

3. Given:

i. dpdt=20 kpamin.

ii. V = 600 cm3

iii

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