Question

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10–6 °C–1.

Answer 1

The range of temperature in which the experiment can be performed with this metre scale is $\bold{15^{\circ}C}$   to  $\bold{25^{\circ} C}$

Explanation:

Given:

Temperature at which accurate reading is given by a metre, $T_1 = 20^{\circ}C$

The admissible variance value, $\Delta L = 0.055 mm = 0.055 \times 10^{-3} m$,

In the longitude, $L_0$= 1 m

Linear expansion ratio for steel, $\alpha = 11 \times 10^{-6}$  $^{\circ}C^{-1}$

Solution:

Let the temperature range within which the experiment can be carried out be $T_2$

We know that

$\Delta L=L_{0} \alpha \Delta T$

$0.055 \times 10^{-3}=1 \times 11 \times 10^{-6} \times\left(T_{1} \pm T_{2}\right)$

$5 \times 10^{-3}=\left(20 \pm T_{2}\right) \times 10^{-3}$

$20 \pm T_{2}=5$

Either

$\mathrm{T}_{2}=20+5=25^{\circ} \mathrm{C}$

or

$\mathrm{T}_{2}=20-5=15^{\circ} \mathrm{C}$

The experiment can therefore be carried out within the temperature range of $15 ^{\circ}C$ to $25 ^{\circ}C.$