# Markings to indicate length are placed on a steel tape in a room that is at a temperature of 22...

## Question:

Markings to indicate length are placed on a steel tape in a room that is at a temperature of {eq}\rm 22^{\circ} C {/eq}. Measurements are then made with the same tape on a day when the temperature is {eq}\rm 27^{\circ} C. {/eq} Are the measurements too long, too short, or accurate?

## Expansion:

When the temperature of the material is increased, the length of the material increases. This increase in the length of the material is due to the expansion of the material because of change in temperature of the material.

The change in length of the material due to increase in the temperature is given by,

{eq}\Delta L = \alpha \Delta T L {/eq}

Where, {eq}\alpha {/eq} = Coefficient of linear expansion

{eq}\Delta T {/eq} = Change in temperature

{eq}\Delta L {/eq} = change in length

L = Original length

When the temperature of the steel material is increased. The heat energy is given to the steel tape. Due to increase in energy of the material, the molecules vibrates with larger amplitude. This results in thermal expansion of the material.

The expansion of the length of the material is given by,

{eq}\Delta L = \alpha \Delta T L {/eq}

Let's assume that the initial length of the steel tape is 1 m.

Thus, {eq}L = 1 m {/eq}

{eq}\Delta T= 27-23=4^{0} C {/eq}

The coefficient of linear expansion of steel, {eq}\alpha = 11 \times 10^{-6} / ^{/circ}C {/eq}

{eq}\Delta L = \alpha \Delta T L=11 \times 10^{-6} \times 4 \times 1 = 44\times 10^{-6} m {/eq}

The change in length of 1 m wire is {eq}44\times 10^{-6} m {/eq}

Thus, the steel tape expands, the observation made by the observer falls short.