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Physics Question on thermal properties of matter

The standard of length is maintained by a 1 meter long bar made up of a material having coefficient of linear expansion α=0.00001∘C−1\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

±0.01∘C\pm 0.01 {^{\circ}C}

B

±0.1∘C\pm 0.1 {^{\circ}C}

C

±0.001∘C\pm 0.001 {^{\circ}C}

D

±0.0001∘C\pm 0.0001 {^{\circ}C}

Answer

±0.1∘C\pm 0.1 {^{\circ}C}

Explanation

Solution

Given, length of bar =1 m=1\, m and coefficient of linear expansion α=0.00001∘C−1\alpha=0.00001^{\circ} C ^{-1} So, expansion of 1 m1\, m length ΔL=1α=1×0.00001∘C−1\Delta L=1 \alpha=1 \times 0.00001^{\circ} C ^{-1} ΔL=10−5∘C−1\Delta L=10^{-5 \circ} C ^{-1} Since, the accurace =1 ppm=±10−6=1\,ppm =\pm 10^{-6} Hence, the maximum allowed temperature variation ±ΔT=10−610−5∘C−1=±0.1∘C\pm \Delta T=\frac{10^{-6}}{10^{-5 \circ} C ^{-1}}=\pm 0.1^{\circ} C