Question

relation between linear coefficient and volume coefficient

Answer 1

1. The problem statement, all variables and given/known data If a solid material is in the form of a block rather than a rod, its volume will grow larger when it is heated, and a coefficient of volume expansion beta defined by β = V 2 − V 1 V 1 ( t 2 − t 1 )
β=V2−V1V1(t2−t1) may be quoted.
Here V 1 V1 and V 2 V2 are the initial and final volumes of the block,
and t 1 t1 and t 2 t2 are the initial and final temperatures. Find the relation between the coefficients α α and β β .

2. Relevant equations α = L 2 − L 1 L 1 ( t 2 − t 1 )

α=L2−L1L1(t2−t1)

3. The attempt at a solution I'm assuming I need to set

V 1 = L 1 W 1 H 1 V1=L1W1H1 and
V 2 = L 2 W 2 H 2 V2=L2W2H2 and
attempt to extract L 2 − L 1 L 1 ( t 2 − t 1 ) L2−L1L1(t2−t1) from L 2 W 2 H 2 − L 1 W 1 H 1 L 1 W 1 H 1 ( t 2 − t 1 ) L2W2H2−L1W1H1L1W1H1(t2−t1)
I've only gotten so far: W 1 H 1 B = L 2 W 2 H 2 − L 1 W 1 H 1 L 1 ( t 2 − t 1 ) W1H1B=L2W2H2−L1W1H1L1(t2−t1) but I can't figure out the rest of the algebraic manipulation. 

Answer 2

Answer:

Coefficient of Linear Expansion : It is the change in length per unit length per unit change in temperature. Coefficient of Volume Expansion:It is the change in volume per unit volume per unit change in temperature.