Question

A manganese sheet of dimensions $20\text{cm}\times 30\text{cm}$ at $25{}^{\circ }\text{C}$ is heated to $75{}^{\circ }\text{C}$, if the area of the sheet is increased by $0.72{\text{cm}}^2$, what is the coefficient of superficial thermal expansion of manganese?

• A. $32\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$
• B. $24\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$
• C. $41\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$
• D. $18\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$

Answer 1

The correct option is B $24\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$

Given:
The initial dimensions of the manganese sheet, $20\text{cm}\times 30\text{cm}⟹$ Initial area, ${\text{A}}_0=20\times 30=600{\text{cm}}^2$
Increase in the area, $\Delta \text{A}=0.72{\text{cm}}^2$
The rise in temperature, $\Delta \text{T}=75-25=50{}^{\circ }\text{C}$
We know that the coefficient of superficial thermal expansion, $\beta$ is given by:
$\beta =\frac{\Delta \text{A}}{{\text{A}}_0\Delta \text{T}}$

$⟹{\beta }_{\text{Mn}}=\frac{0.72}{600\times 50}$

$⟹{\beta }_{\text{Mn}}=2.4\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$

$⟹{\beta }_{\text{Mn}}=24\times {10}^{-6}{}^{\circ }{\text{C}}^{-1}$