Question

On Cubical Expansion
(A)Length increases
(B)Breadth increases
(C)Both
(D)None

Answer 1

When the volume of the body increases due to heating the expansion is called a cubical or volumetric expansion. On hearing a solid there is an increase in its length, breadth, and thickness so, we consider expansion in volume is called a cubical expansion. An example of cubical expansion is turning the water into the stream on boiling. Find the answer to this question by solving the below equations.

Complete step by step solution:
Consider the volume of a solid body${V_0}$ at temperature${0^ \circ }C$. Let the body heat to some higher temperature ${t^ \circ }C$. Let $V$ be the volume of the body at temperature ${t^ \circ }C$.
$\therefore$Change in temperature $= {t_2} - {t_1} = t - 0 = t$
And Change in volume $= V - {V_0}$
Experimentally it is found that the change in the volume $(V - {V_0})$is
Directly proportional to the original volume $({V_0})$,
$\Rightarrow V - {V_0} \propto {V_0}.......\left( 1 \right)$
Directly proportional to change in the temperature $\left( t \right)$,
$\Rightarrow V - {V_0} \propto t......\left( 2 \right)$
Dependent upon the material of the body,
From equation$\left( 1 \right)\& \left( 2 \right)$
$\Rightarrow V - {V_0} \propto {V_0}t$
$\Rightarrow V - {V_0} = \gamma {V_0}t....\left( 3 \right)$
Where ‘$\gamma$’ is a constant called a coefficient of cubical expansion.
$\Rightarrow \gamma = \dfrac{{V - {V_0}}}{{{V_0}t}}$
This is an expansion for the coefficient of cubical expansion of a solid.
The coefficient cubical expansion is defined as an increase in volume per unit original volume at ${0^ \circ }C$ per unit rise in temperature.
From the equation$\left( 3 \right)$we get,
$\Rightarrow V = {V_0} + \gamma {V_0}t$
$\therefore V = {V_0}\left( {1 + \gamma t} \right)$
This is an expression for the body of the volume at ${t^ \circ }C$.
Hence, the correct answer for a cubical expansion is both length and breadth increase.

Note: The cubical expansion is defined as the increase in the volume of a substance with a change in temperature or pressure.
The increase in the volume of a unit volume of solid, liquid, or gas for a rise of temperature of ${1^ \circ }C$ at constant pressure is called as the coefficient of expansion or coefficient of thermal expansion or coefficient of volumetric expansion or expansion coefficient.