# Thermal Expansion

## Objectives

• Measure the expansion vs. temperature of a copper tube, and use this to determine its expansion coefficient
• Do the same for at least one other tube of a different material
• Compare the expansion coefficients to known values for the materials

## Resources

• Linear expansion apparatus
• Copper, aluminum and steel tubes
• Steam generator, hoses
• Thermistor sensor and clamp
• ScienceWorkshop interface and Datastudio software
• Datastudio setup file expansion.ds

## Background

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In general, matter expands upon heating and contracts upon cooling. Although this effect is greatest for gases, it cannot be neglected for solids, e.g. in the design of machinery and roads. On a molecular level, temperature corresponds to the kinetic energy of the individual molecules in a substance. In a solid material, the molecules have kinetic energy in the form of vibration. As temperature increases, so does the amplitude of this vibration, causing the space between the molecules to expand in a very uniform way, at least for a certain range of temperatures.

The change in length of a material of length $L$ when its temperature changes by $\Delta T$ is given by $$\Delta L = \alpha L \Delta T$$

Where $\alpha$ is the linear expansion coefficient.

## Procedure for Heating Tubes

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The tubes you will heat are mounted in a special bracket so that one end of the tube is fixed and the other can press against a spring arm connected to a dial gauge that displays the position of the spring arm in fractions of a millimeter. Water is heated an electric kettle to produce steam, which is funneled through a hose and into one end of the metal tube. A thermistor (i.e. a temperature-sensitive resistor) is clamped against the tube as it heats, and the temperature is tracked with DataStudio.

1. Turn on the steam generator and turn the temperature knob up to full. Wait until the water is boiling before connecting the hose between the water tank and metal tube.
2. When you are ready to heat the tube, connect the hose between the water tank and one end of the tube.
3. Tilt the hose end of the metal tube upward using a wooden block. Place a styrofoam cup at the other opening of the tube to catch condensed steam.

## Spring Dial Gauge

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The spring dial gauge shows the position of the spring arm. The dial has a range of 10mm. The large hand shows increments of 0.01mm, and the small hand gives increments in millimeters.

## Hints

Hint 1:

Gently push on the spring arm of the dial gauge to see what happens. This will give you a better feel for what the dial is measuring.

Hint 2:

When measuring the initial length of the bar, you should exclude the small bit between the metal tab and the end. Why?

Hint 3:

Make sure one of your group members watches the dial for the entire time the bar is being heated. It’s easy to miss the motion of the smaller needle