volume expansion formula?

Question

hi..can u plz help me with my report?
what is the formula for volume expansion?
and can u explain it?

Answer 1

Linear expansion due to temperature change is defined as

dL=k L (T2-T1)

dL - change in length
k - coefficient of linear expansion
L - length at T1
T2 - final temperature
T1 - initial temperature

A volume will change in thee dimentions so for rectangular prism of volume V=a x b x c we can write

V1=a x b x c
V2=(a + da) (b + db) (c + dc)
da= k a (T2-T1)
and so on... so
V2=(a + k a (T2-T1)) (b + k b (T2-T1)) (c + k c (T2-T1))=
V2=a b c (1+k (T2-T1)) (1+k (T2-T1)) (1+k (T2-T1))
finally
V2=a b c (1+k (T2-T1))^3

I hope it helps