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Question

Which best expresses the value for the coefficient of volume expansion, β, for given material as a function of its corresponding coefficient of linear expansion, α?

a. β=α^3
b. β= 3α
c. β=α^2
d. β=2α

Reason why?

Answer 1

Wow, so many answers, so little quality.

Look, guys, here's how it's done:

The linear expansion of a material is given by

δx = x(αδT)

were δx is the change in length, x is the original length, α is the coefficient of linear expansion (in units of "per temperature") and δT is the temperature change.

That means the final length is given by:

xf = x+δx = x (1+αδT)

Now let's consider the new volume (scaling in x, but to be pedantic you should use x,y,z; it doesn't change either way):

V = (xf)³ = (x+δx)³ = x³(1+αδT)³

Now pay attention, kids, because this is important:

Expanding the parenthetical term gives you terms in α, α² and α³. The only ones worth keeping are the terms in α, because αδT<<1. That means,

(1+αδT)³ ≈ 1+3αδT (expand it out if you don't believe me).

This means,
V ≈ x³(1+3αδT),

and the _right_ volume-expansion substitution is

V ≈ x³(1+βδT)
or β=3α

Sheesh!

Good luck, work hard, and stay away from drugs.

Answer 2

MikeyZ's answer below is 100% correct.

Thumbs up for Mikey. Give him the Best Answer award!

Check out the Wikipedia link below.

b. β= 3α

Answer 3

a..ß=α³ ...
Linear expansion is expansion in Length.
Cubical expansion is in all directions..Volume.

In fact, cubical expansion = linear expansion x 3

Answer 4

she walked for a million hour at v km/h, and cycled for 2 hours at 3v km/h. a million v km/h + 2(3 v km/h)= fifty six km 7 v km/h = 56km fifty six/7 km/hr became into her velocity the straight forward velocity is (168/7)(2)+(fifty six/7)=224/7=32 km/h

Answer 5

d) b=2a

because, a is the leniar expansion and b is the area, and therefore, the leniar expansion in B is added

Answer 6

a

Answer 7

a. Volume is a cubic quantity...