lab10-temperatureandlinearexpansion

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Physics 211 Lab 10

Temperature Scales and Linear Expansion

Introduction: In this lab you will measure and record temperature data to determine the

relationship between the Fahrenheit and Celsius scales. You will plot and analyze the data using

a spreadsheet. Also, the thermal expansion of some metals will be investigated and their

coefficients of linear expansion determined. Although this effect is small, it is important in

many material applications. For example, a piston could stick in its cylinder, a rivet could

loosen, or a bridge girder could produce damaging stress.

Theory:

Review of Linear Relationships: Experiments are normally planned so that only one quantity is

varied at a time. The varied quantity is called the independent variable. The measured quantity is

called the dependent variable, because its value depends on what you have done with the

independent variable. Customarily, the independent variable is placed on the x-axis and the

dependent variable on the y-axis.

A line, such as the one shown in Figure 1, that is drawn between experimental linear data points

is called a best-fit line, or sometimes as regression line.

Figure 1 best fit line

A best-fit-line does not go directly from point to point, but rather averages out measurement

errors by minimizing the total error from each individual data point. The best-fit-line allows for

the prediction of data points in places where no experimental data was collected. All linear

relationships can be described by the general equation:

y = mx + b where12

12

xx

yym

=

Here x and y are the experimental quantities measured, and m (slope) and b (y-intercept) are

constants defining the linear relationship between the two quantities.

Fahrenheit and Celsius temperature scales: The Fahrenheit temperature scale is still widely

used in the United States. However, the rest of the world and the scientific community in the

0

1

2

3

4

5

6

0 2 4 6 8 1 0 1 2


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United States use the Celsius temperature scale. Fortunately, a definite linear relationship exists

between these two temperature scales. Using this relationship, conversions between the two

temperature scales can easily be accomplished:

32)(8.1)( += CTFT or

8.1

32)()(

=

FTCT

Thermal Expansion: In solids, a temperature change leads to the expansion of a body as a

whole. (A contraction resulting from a temperature decrease is a negative expansion.) The

change in the solids, length, width, or thickness, is called linear expansion for any one of its

dimensions. This may be different for different directions; however, if the expansion is the same

in all directions it is referred to as isotropic expansion. The expansion is a metal rod is shown

in Figure 2.

Lo

L

L

Figure 2 Linear expansion of a solid

The fractional change in length L/L0, whereL0 is the length of the object at the initial

temperature T0, is related to the change in temperature Tto a good approximation by

L/L0 = T

Here L = L L0 (the change in length), T = TT0 (the change in temperature), and is the

coefficient of linear expansion (sometimes called the thermal expansion coefficient), with units

of inverse temperature (1/0C). The coefficient of linear expansion, , is very nearly constant

over a wide temperature range.

Solving the equation above for defines it in terms of experimentally measurable quantities

= L/( L0T)

Hence, by measuring the initial lengthL0 of an object (e.g., a metal rod) at an initial temperature

T0 and the change in its length L for a corresponding temperature change T, can be

computed.

Rod at T = T1

Rod at T = T + T


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Experimental Procedure

Part 1 Temperature Scales

1. Fahrenheit/Celsius Experiment

A. Obtain a water container and fill it about half full. Obtain a thermometer calibrated in both the

Fahrenheit (oF) scale and the Celsius (

oC) scale. Measure the temperature of the water on both

temperature scales. Record the temperature readings and label the time as 0.

B. Hook up the electric stove top coil. Place the container of water on the coil and start timing

your experiment. Make sure that the bottom of the thermometer is not resting directly on

the bottom of the container.

C. As the water begins to warm up, record the temperature in bothoF and

oC at two-minute

intervals. Fifteen seconds before you take a reading begin to stir the water with the thermometer

to make for a uniform temperature. Record the time since the experiment began and temperatureon the report sheet. Do not touch the copper container. It will become very hot!

D. Once you have 6 data points turn off the electric coil. Remove the thermometers and allow the

hot water and copper container to cool before you disassemble the set-up.

2. Graph Your Data Using a Spreadsheet

A. Open Microsoft Excel on the computer and enter your data in the first two columns. Put the

Celsius readings in the first column. Include an appropriate column label on the first line of

each column.

B. Now select the headings and data you typed into the columns and choose the chart wizard.

Make an XY scatter graph by following the steps in the wizard. Then, perform a linear fit on

your data to obtain the slope of the curve by right clicking on the data set and choosing Add

Trend Line. Make sure the linear fit equation shows by choosing Options Show Equation.

Find the percent error between your value and the theoretical value from the theory section of

the lab. Print your data and graph.

Part 2 Thermal Expansion

1. Obtain a steam generator, an electric hot plate, rubber tubing, a Styrofoam cup, a meter stick,

a Celsius thermometer, a metal rod, and the steam jacket apparatus with a micrometer

attachment for measuring L of the metal rod. A thermometer in the steam jacket measures

the temperature of the rod. Steam is supplied to the jacket by a steam generator and a beaker

is used to catch the condensate.

2. Before assembling the apparatus, measure the lengths (LO) of the metal rods with a meter

stick to the nearest 0.1mm and record these lengths. Avoid handling the rods with your bare

hands in order not to raise their temperature. Use a paper towel or cloth.


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3. Assemble the apparatus, placing one of the rods in the steam jacket. Initially have one end ofthe rod placed firmly against the fixed end screw and the other end not touching the

micrometer screw. Carefully turn the micrometer screw until it just makes contact with the

rod. Do not force the screw. Record the micrometer setting. Do this three times and take the

average as the initial setting. As soon as the initial micrometer setting is taken, read andrecord the initial temperature T0. Then, wet a rubber stopper and carefully insert the

thermometer bulb through it so the entire bulb emerges from the small end of the stopper.

4. Turn the micrometer screw back from the end of the rod several millimeters to allow for the

thermal expansion of the rod with increasing temperature. With the steam generator about

one-half full, turn on the hot plate and boil the water. Attach the rubber tubing to theapparatus so that steam passes through the jacket. Caution: Be careful not to burn yourself

with the condensed hot water in the steam jacket, the steam jacket itself, or the copper

container. Place the thermometer in the steam jacket so that is just touches the metal rod.

Allow steam to pass through the jacket until the thermometer reading stabilizes (this may

take about 15 minutes).

5. When equilibrium has been reached, record the thermometer reading. Then carefullyadvance the micrometer screw until it touches the end of the rod and record the micrometer

setting. Do this three times and take the average of the micrometer readings. Turn off the

heat source.

6. Repeat procedures 3 and 4 for two other types of metal rods. Caution: Be careful not to burn

yourself with the condensed hot water in the steam jacket, the steam jacket itself, or the hot

rod when you remove it.

7. Compute

L and

T, and find the coefficient of linear expansion for each metal.

Questions

1) Compare your computeroC/

oF graph equation to the exact equation. What factors could

account for a slightly different equation for the lines?

2) Convert the following temperatures to oC. Equation used: __________________________

70oF=_____________ oC 100oF=____________ oC 20 oF=_____________ oC

3) Convert the following temperatures to oF. Equation used: __________________________

320C = oF 20oC = oF 25oC = oF

4) Compare your values for the thermal expansion coefficient of the different metal samples with

the accepted values by computing the percent errors.


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Name _____________________________

Report Sheet for Lab 10 Temperature and Linear Expansion

Part 1 Temperature Scales

Use Microsoft EXCEL to record and graph your data

Calculate % error in slope of line here:

Part 2 Thermal Expansion

Metal # 1

Initial Values Lo = ____________ To = ____________

Length Change L Initial Readings: ________ _________ _______ Avg: ___________

Final Readings: ________ _________ _______ Avg: ___________

L = Final Initial = ___________

Temp Change T T = Final Initial = ___________

Calculation of Linear Expansion Coefficient for Metal # 1


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Metal # 2







Metal # 3







lab10-temperatureandlinearexpansion

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