Question

Define thermal expansion for alpha, beta and gamma.
A) $\alpha :\beta :\gamma ::1:3:2$
B) $\alpha :\beta :\gamma ::3:2:1$
C) $\alpha :\beta :\gamma ::2:3:1$
D) $\alpha :\beta :\gamma ::1:2:3$

Answer 1

Hint: The thermal expansion is majorly of three types- linear, area and volume. The thermal coefficients are expressed by $\alpha $,$\beta $ and $\gamma $. The volume is three times the length and area is twice the length.

Complete step by step answer:
The thermal expansion is defined as the expansion produced when they are heated. The length wise expansion in metals is called linear expansion and that of surface wise and volume wise are called as surface and volume expansion respectively. Coefficient of linear expansion is given by the expression ${{\Delta l} \over l} = \alpha \Delta T$. Now the area is equal to the square of length. So the coefficient of surface expansion will be given as,
$A + \Delta A = {(L + \Delta L)^2}$
$\Rightarrow {L^2} + 2L\Delta L + {(\Delta L)^2}$
$\approx {L^2} + 2L\Delta L $
$\Rightarrow A + 2A(\dfrac{\Delta L}{L})$
From this equation we get, $\dfrac{\Delta A}{A} = 2\dfrac{\Delta L}{L}$
which is equal to, $\beta = 2 \alpha$
Similarly we can prove for the coefficient of volume expansion which will give $\gamma = 3\alpha $.
 On finding the ratio of coefficients we get $\alpha :\beta :\gamma ::1:2:3$.
These coefficients give the measure of the metals upto which they can expand linearly, superficial or volumetric.

Note: The volumetric expansion is thrice the linear expansion and surface expansion is twice the linear expansion. This expansion is done in metals because they have the property to expand on heating. The metals expand in all directions.