The linear expansion coefficient of a solid?

I%26#039;ve wrongly put the category into mathematics room..


So, I would like to ask again..





Generally, the length of a solid bar changes according to temperature changes. The change of the length 螖l according to temperature is proportional to the change of temperature 螖T. In addition, it is proportional to the initial length of bar.





But, my questions are:





1) What is the case that the length change isn%26#039;t exactly proportional to the temperature change?





2) How to verify the coefficient of the volume expansion 尾鈮?伪?





3) How to check the quality of each sample bar from the measured linear expansion coefficient?





I%26#039;m having physics lab tomorrow and we%26#039;re supposed to hand in the answer sheet by tomorrow.


So, can anyone help me? Thank you so much..|||1. It isn%26#039;t exactly proportional, it is usually a very slightly curvy graph for any given material, since temperature is defined by fixing 0 degrees and 100 degrees and drawing an (artificial) straight line between them. This is one reason why good thermometers were once so hard to make. Nevertheless, to a good approximation it is linear.


2. It%26#039;s an approximation for most simple solid materials: three dimensions means roughly one third of the expansion (proportionally) goes in each direction. That%26#039;s all it means.


3. Comparing the theoretical expansion with the one observed could demonstrate the presence of impurities. The bigger the disparity the more impure.