how is linear,volume, area expansion be solved?

Question

can you please give me samples problems about linear expansion, volume expansion and area expansion? together with the sample problems are the solutions of how'd you get the answer. thank you!

Answer 1

The principle of linear expansion, at least at the macro level, is quite simple. It is being governed by


Charge in length dL=C L (T2-T1)
C - coefficient of liner expansion
L - length at temperature T equal to T1
T2 - temperature at which the length has changed

Area and volume expansion are derived from linear expansion.

Let's say we have a rectangle of one edge equal to a and the other to b.

dA=A2-A1= [a+da][b+db] - ab
dA=ab + a(db) + b(da) + (da)(db) - ab
dA=a(db) + b(da) + (da)(db)

da=C a (T2-T1)
db=C b (T2-T1)

dA=a(C b (T2-T1)) + b(C a (T2-T1)) + (C a (T2-T1))(C b (T2-T1))
dA= C(T2-T1)[(ab + ab + abC(T2+T1)]
dA=C ab (T2-T1)[2+C(T2+T1)]

As you can see the best way is to solve these problems algebraically.

I hope it helps