Concept explainers
a.
Find the rate of change of volume with respect to pressure.
a.
Answer to Problem 21E
Explanation of Solution
Given information:
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant:
Calculation:
The equation that models the volume can be wriiten as
b.
Is the volume decreasing more rapidly at the beginning or the end of the
b.
Answer to Problem 21E
The volume is decreasing most rapidly at the beginning, when
Explanation of Solution
Given information:
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant:
A sample of gas is in a container at low pressure and is steadily compressed at constant temperature for
Calculation:
The equation that we just found for change volume indicates that as the pressure gets larger constant temperature, the rate at which the volume changes deceases.
Hence, the volume is decreasing most rapidly at the beginning, when
c.
Prove that the isothermal compressibility is given by
c.
Answer to Problem 21E
Explanation of Solution
Given information:
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant:
Calculation:
Isothermal compressibility is defined as
We know that
Hence, proved.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning