Question

The standard of length is maintained by a 1 meter long bar made up of a material having coefficient of linear expansion $\alpha = 0.00001 {^{\circ}C^{-1}}$. If the length of the bar were to be preserved to an accuracy of 1 part per million, what would be maximum allowed temperature variation?

• A. $\pm 0.01 {^{\circ}C}$
• B. $\pm 0.1 {^{\circ}C}$
• C. $\pm 0.001 {^{\circ}C}$
• D. $\pm 0.0001 {^{\circ}C}$
• E. $\pm 1.0 {^{\circ}C}$

Answer 1

Answer: (B)

Given, length of bar $=1\, m$ and coefficient of
linear expansion $\alpha=0.00001^{\circ} C ^{-1}$
So, expansion of $1\, m$ length
$\Delta L=1 \alpha=1 \times 0.00001^{\circ} C ^{-1}$
$\Delta L=10^{-5 \circ} C ^{-1}$
Since, the accurace $=1\,ppm =\pm 10^{-6}$
Hence, the maximum allowed temperature variation
$\pm \Delta T=\frac{10^{-6}}{10^{-5 \circ} C ^{-1}}=\pm 0.1^{\circ} C$