Question

When the temperature of a copper coin is raised by ${80}^0$ C, its diameter increases by $0.2\%$

• A. percentage rise in the area of a face is $0.4\%$
• B. percentage rise in the thickness is $0.4\%$
• C. percentage rise in the volume is $0.6\%$
• D. coefficient of linear expansion of copper is $0.25\times {10}^{-4}{/}^{0}C$

Answer 1

Answer: (A), (C), (D)

percentage rise in the area of a face is $0.4\%$
percentage rise in the volume is $0.6\%$
coefficient of linear expansion of copper is $0.25\times {10}^{-4}{/}^{0}C$

Percentage increase in diameter is given by

$\frac{△l}{l}\times 100=\alpha △T\times 100=0.2\%$--------(1)
$\Rightarrow \alpha △T\times 100=0.2\%$
$\Rightarrow \alpha =\frac{0.002}{△T\times 100}=\frac{0.002}{80\times 100}=0.25\times {10}^{-4}{/}^{0}C$

Now, percentage change in Area is given by,
$\frac{△A}{A}\times 100$$=\beta △T\times 100$
Putting values from equation (1):
$\Rightarrow \frac{△A}{A}\times 100$$=2\alpha △T\times 100$

$\frac{△A}{A}\times 100=2\left(0.2\right)\frac{△A}{A}\times 100=0.4\%$

$0.4\%$ is the percentage rise in Area.
$\frac{△V}{V}\times 100$$=\gamma △T\times 100=3\times \alpha △T\times 100$
$\frac{△V}{V}\times 100=3\left(0.2\right)\frac{△A}{A}\times 100=0.6\%$
$0.6\%$ is the percentage rise in volume.