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The first real length standard, adopted more than 200 years ago, was a platinum bar with two very fine marks separated by what was defined to be exactly one meter. If this standard bar was to be accurate to within ±1.0μm, how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion is 9×106/C .

Short Answer

Expert verified

The required temperature isΔT=±0.11C.

Step by step solution

01

Given data

The standard bar should be withinΔL=±1.0μm.

The coefficient of linear expansion isα=9×106/C.

The length is L=1m.

02

Expression for linear expansion

In this problem, use the expression for the linear expansion of a material to determine the temperature required.

03

Calculation of the temperature

The relation to find the requiredtemperature can be written as:

ΔL=αLΔT

Here,ΔTis the required temperature.

On plugging the values in the above relation, you get:

(1μm×106m1μm)=(9×106/C)(1m)ΔTΔT=±0.11C

Thus, ΔT=±0.11Cis the required temperature.

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