Chapter 12, Problem 4RQ

You are experimenting with several liquid metal alloys to find a suitable replacement for the mercury used in thermometers. You have attached capillary tubes with a circular cross section and an inside diameter of 0.3 millimeters to reservoirs containing 5 cubic centimeters of each alloy. You mark the position of the liquid in each capillary tube when the temperature is 20 degrees Celsius, systematically change the temperature, and measure the distance the liquid moves in the tube as it expands or contracts with changes in temperature. Note that negative values correspond to contraction of the material due to lower temperatures. The data you collected for four different alloys is shown in the following table.

1. a. In Excel, create two new columns for each compound to calculate the change in temperature (∆T) relative to 20 °C (for example, 25 °C gives ∆T = 5 °C) and the corresponding change in volume (∆V).
2. b. Plot the change in volume versus the change in temperature: fit a linear trendline to each data set.
3. c. From the trendline equations, determine the value and units of the coefficient of thermal expansion, β, for each alloy. Note that ∆V = βV∆T, where V is the initial volume.
4. d. There is a small constant offset (C) in each trendline equation (∆V = βV∆T + C). What is the physical origin of this constant term? Can it be safely ignored? In other words, is its effect on the determination of β negligible?