Solution Found!
Show that for an isotropic solid, ? = 3?, if the amount of expansion is small. ? and ?
Chapter 13, Problem 19P(choose chapter or problem)
(III) Show that for an isotropic solid, , if the amount of expansion is small.
and
are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13-30.]
Questions & Answers
QUESTION:
(III) Show that for an isotropic solid, , if the amount of expansion is small.
and
are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13-30.]
ANSWER:
Solution 19 P
Step 1 of 3
We have to show that for an isotropic solid,.
and
are the coefficients of volume and linear expansion respectively.
Let the isotropic solid be cuboidal in shape with length of each dimension as The volume of the cube is
.
The change in the volume of cube which undergoes a temperature change is given by,
. . . . . (i)
where,
coefficient of volume expansion
original volume in m3
change in temperature in oC