# Coefficient of Volume Expansion: A Water Thermometer.

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### The Idea

All materials (with the one notable exception of ice at around 4°C) expand when heated. It is hard to notice the difference in volume between a hot cup of tea and the volume in the cup when the tea cools. This experiment gives a way to intensify the effect of the thermal expansion, so it can be measured and compared to a known value.

### What You Need

• 250 mL flask
• 2-hole rubber stopper that fits in the flask
• hotplate
• 1000 mL beaker (or one large enough for you to place the flask in)
• glass tube that fits through the rubber stopper (about 15 inches long)
• water
• glass thermometer that fits through the second hole of the stopper (if you don't have a thermometer that works, then you need a one-hole stopper)
• Vaseline (or glycerin) and a towel to help slide the glass and the thermometer into the stopper
• ruler
• ring stand with a beaker or test tube clamp

### Method

1. Determine the radius of the glass tube by:
• Partially filling the glass tube with water. Place your finger over the top of the tube to keep the liquid from sliding out while you are making this measurement.
• Measure the height, ho, of the water column.
• Release the volume into the graduated cylinder and measure the volume.
• The volume of the liquid measured V = π r2.
• The radius of the tube is r = (V/πho)½.
2. Carefully slide the glass tube into the stopper. Use a little Vaseline or glycerin as a lubricant and protect your hands with a towel as you push. Don't force it. A few inches of the tube should extend below the stopper with the rest sticking out above.
3. Slide the thermometer into the other hole, so the bottom of the thermometer is positioned near the center of the flask.
4. Completely fill the flask with water. (Add food coloring if you like—your choice of color.)
5. Insert the stopper. A small amount of liquid may spill out over the side of the flask and some may be forced up the tube.
6. Place the flask with the stopper in the beaker.
7. Fill the beaker with water to cover the flask.
8. Place the beaker on the hot plate.
9. Turn on the hotplate. The apparatus for this experiment is pictured in Figure 90-1.
10. Record the temperature in the flask and note the position of the liquid in the glass tube. (If you have a Sharpie handy, mark it on the glass.)
11. When the temperature in the flask rises a few degrees, record the temperature and measure the increase in the height of the liquid in the flask.
12. The increase in volume for a given temperature increase is given by V = π hr2, where h is the measured height (in meters) and r is the inner radius of the glass previously. In setting this up, some liquid likely will extend into the tube at your starting temperature. If this is the case, define this as your zero point and take h as the distance the liquid rises into the tube. (The small difference in volume resulting from the liquid that initially rises into the tube is not significant for this measurement, but if you are very picky, you can correct for this on principle.)

### Expected Results

A given volume of water expands by a factor that is 0.000207 (or 2.07 × 10–4) of its original volume for every 1 degree increase centigrade. This volume is distributed between the flask and the tube.

### Why It Works

Nearly all materials expand when they are heated. The amount of expansion is characterized by something called the coefficient of expansion. In the case of solids, the expansion in one direction is called the coefficient of linear expansion. Multiplying the original length by the coefficient of linear expansion gives how much longer the object is.

Volume works almost the same way, except in the three dimensions. The coefficient of volume expansion indicates how much volume is added to a (solid or liquid) material for every degree the temperature increases.

### Other Things to Try

Design and calibrate a water thermometer using the coefficient of volume expansion for water and the dimensions you determined for the glass tube.

### The Point

The amount a material expands when heated is called the coefficient of volume expansion. We constrained the expansion of a larger volume of water in the flask to primarily one dimension in the tube. This magnified the effect of the expansion, so we were able to measure it.