# D1-1: Linear Expansivity¶

## Apparatus¶

Gas burner or a stove; heating stand; steam generator; expansion sample; small beaker or dish; meter stick; micrometer; thermometer; stack of books, table of linear expansivities of common materials

## Procedure¶

1. Set up apparatus as shown above. Be sure the sample slopes away from the steam generator, screw #1 is very tight, and screw #3 is very loose. Be certain there is water in the steam generator.
2. Loosen screw #2 and push the sliding metal piece up against the leg which holds the sample. Tighten screw #2 to lock the sliding metal piece in this position. Measure the distance $$AB$$ with a micrometer. NOTE: The metal faces at $$A$$ and $$B$$ are not perfectly flat or parallel. You must measure $$AB$$ at the very edge of the metal pieces and then use the exact same location for all future measurements.
3. Measure the length, $$L_0$$,of the sample. Measure from the centers of the tightened screws #1 and #2.
4. Measure the room temperature.
5. Light the gas burner or stove. After steam begins flowing steadily through the tube wait 3 minutes and then measure $$AB$$ again.

## Observations¶

$$AB$$ before heating = ________ m

$$AB$$ after heating = ________ m

$$\Delta L$$ = change in length = ________ m

$$L_0$$ = length of sample between screws 1 and 2 = ________ m

$$\Theta_T$$ = room temperature = ________ °C

$$\Delta \Theta$$ = change in temperature of the sample = ________ °C

## Theory¶

The coefficient of linear expansion is determined from the relation $$\Delta L = L_0 \alpha \Delta \Theta$$ where $$\alpha$$ is the average of the coefficient of linear expansion over the temperature range.

## Analysis¶

1. What is the coefficient of linear expansion of the sample?
2. What material is the sample? Explain your choice by refering to a table of linear expansivities of common materials.
3. List 4 assumptions you made in determining the coefficient for the sample. For each assumption justify it or account for error.