relation between coefficients of thermal expansion

[arunmrao]

It is regarding the relation between coefficient of thermal expansion i.e alpha:beta:gamma which is1:2:3.I have forgotten the derivation of this relationship. Can someone help me out. I need to teach my school going son. Thanks in anticipation

 

[prex]

I suppose you mean with alpha the linear expansion coeff., with beta the area exp.coeff. and with gamma the volumic one.
The derivation is simple.
For example in the 2D case, the new length in x direction is proportional to
1 + alpha T
and the same in y direction.
The new area will hence be proportional to
(1 + alpha T)^2
or, as (alpha T) will normally be small with respect to 1, to
1 + 2 alpha T
neglecting the sqare of (alpha T).
A similar derivation gives
gamma=3 alpha
for the 3D case.


prex
motori@xcalcs.com

http://www.xcalcs.com

Online tools for structural design

 

[arunmrao]

Thanks for your assistance, I was not certain about the assumption that the value being small can be ignored as it is near zero. To physically explain this assumption I stumbled. But as you confirm the only way out is that it should be memorized. Thanks once again.

Dr Arun Rao