   Chapter 10, Problem 20P

Chapter
Section
Textbook Problem

Show that the coefficient of volume expansion, β, is related to the coefficient of linear expansion, α, through the expression β = 3α.

To determine
The relation between the co-efficient of linear expansion ( α ) and co-efficient of volume expansion ( β ).

Explanation

Formula to calculate the volume of a solid at a temperature T0 is,

V0=A0L0

• A0 is the cross sectional area.
• L0 is the length of the solid.

When there is a change in temperature, A0 and L0 also change.

The change in temperature is,

ΔT=TT0

The area (A) at temperature T is,

A=A0(1+2αΔT)      (I)

The length (L) at temperature T is,

L=L0(1+αΔT)       (II)

Formula to calculate the volume of a solid at a temperature T is,

V=AL       (III)

Substitute Equations (I) and (II) in (III).

V=A0L0(1+2αΔT)(1+αΔT)

Substitute V0 for A0L0 in the above equation

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

The smallest unit of any substance is the _____. a. atom b. molecule c. cell

Biology: The Unity and Diversity of Life (MindTap Course List)

What determines the chemical reactivity of an atom?

Biology: The Dynamic Science (MindTap Course List)

What are sister chromatids?

Human Heredity: Principles and Issues (MindTap Course List)

What organ is the source of glucagon?

General, Organic, and Biological Chemistry

True or false? Some humans are genetically modified.

Biology: The Unity and Diversity of Life (MindTap Course List) 