   Chapter 3.7, Problem 23E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Boyle’s Law states that when a sample of gas is compressed al a constant temperature, the product of the pressure and the volume remains constant: PV = C.(a) Find the rate of change of volume with respect to pressure.(b) A sample of gas is in a container at low pressure and is steadily compressed at constant temperature for 10 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 10 minutes? Explain.(c) Prove that the isothermal compressibility (see Example 5) is given by β = 1/P.EXAMPLE 5  (a)

To determine

To find: The rate of change of volume with respect to the pressure.

Explanation

Given:

The relation of Boyle’s law is given as below.

PV=C

V=CP (1)

Here, P is the pressure, V is the volume, and C is constant.

Calculation:

Rewrite equation (1) as follows.

V=CP1

Differentiate equation (1) with respect to P.

dVdP=C(

b)

To determine

To find: Check the occurrence of the rapid volume decrease of gas at the end or at the beginning of the compression with explanation.

1. a) Prove the isothermal compressibility equation as β=1P.

c)

To determine

To prove: The isothermal compressibility equation as β=1P.

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