Question

show that coefficient of volume expansion is thrice its coefficient of linear expansion​

Answer 1

When any body or object is heated up then the change happens in the expansion coefficients. Here γ is the coefficient of volume expansion and γ ≈3α. Here α is the linear expansion coefficient. Hence, coefficient of volume expansion coefficient is three times of the linear expansion coefficient.

Answer 2

Answer:

The coefficient of volume expansion(γ) is 3 times linear expansion$(\alpha )$.i.e.γ$=3\alpha$

Explanation:

Let the initial dimensions of the solid be l1,l2 and l3

Initial volume(V)=l1×l2×l3        (1)

After heating the final lengths are,

l1'=l1(1+$\alpha$ΔT)        (2)

l2'=l2(1+$\alpha$ΔT)      (3)

l3'=l3(1+$\alpha$ΔT)      (4)

$\alpha$=linear expansion

Final volume after heating(V')=l1(1+$\alpha$ΔT) × l2(1+$\alpha$ΔT) ×l3(1+$\alpha$ΔT)    

V'=V$($1+$\alpha$ΔT$)^{3}$        (5)

The final volume can also be written as,

V'=V(1+γΔT)           (6)

γ=volume expansion

Since $\alpha$ is very small $(^{}$1+$\alpha$ΔT$)^{3}$≈(1+3$\alpha$ΔT)

By equating equations (5) and (6) we get;

V(1+3$\alpha$ΔT)=V(1+γΔT)

γ=3$\alpha$

Hence, the coefficient of volume expansion is thrice its coefficient of linear expansion.