CBSE Class 11-science Answered

the 3 thermal coefficients are : linear, areal and  volume expansions of solids

a:b: y =1:2:3

To show that coefficient of volume expansion is thrice coefficient of linear expansion, consider a cube of side l.

Each side of the cube expands on increasing its temperature. The volume of expanded cube is

V = V₀ (1+γT)

V = L₀³(1+αT)³  = V₀ (1+3α^2T^2+3αT+α^3T^3) 

As α has a very small value its higher powers can be neglected.

Comparing equation i and ii we get

γ = 3α

Similarly a derivation can be done for β