## Thermal Expansion Calculation

Introduction

Calculate the expansion of the length of a rod as it warms.

Materials

Cool Hot Rod set up (the rod rolls a needle through an angle as it expands.)
Meter stick or 1 meter tape.
Protractor
Thermometer
Micrometer

To Do and Notice

Measure the length of the rod between the needle and the clamp, L. Assume L = 1 m.

Measure the diameter of the needle with the micrometer, d. Assume d = 0.25 mm.

Measure the temperature of the rod, room temperature, in Celsius, Tr.

Set the needle indicator vertical.

Measure the temperature of the cold water, if you use ice water it will be Tc = 0°C.

Calculate the temperature change T = Tr-Tc. Perhaps T = 25 °C

Pour cold water through the copper tube.

Notice the needle move, use the protractor to measure the angle the needle rotates through, A. Perhaps A = 30 degrees.

What's Going On?

When the copper cools it contracts.

As it contracts it slides without slipping over the needle causing the needle to roll.

Math Root

If the needle rotated completely around through 360 degrees the rod would have moved one full diameter of the needle, pi*d = 3.14 * 0.25 = 0.8 mm

If the needle moves through the angle, A, then the rod rolled a fraction s = A/360 of the circumference. s = 30°/360 * pi * d = 1/12 * 0.8 = 0.07 mm

We can easily measure fractions of a mm.

What was the fractional increase in length of the rod, F = s/L = 0.00007m/1m = 0.00007

What is the fractional increase in length per degree temperature change f = F/T = F/25 = 0.00007/25 = 0.00002 = 2 x 10^-5 fractional length increase per degree celsius

This is called the coefficient of linear expansion for copper.

The textbook value of the fractional linear expansion coefficient of coppr is is 1.7 x 10^-5 per degree celsius.

 Scientific Explorations by Paul Doherty © 2014 4 June 2014