Question

Experimental data:

Length L0 of the cold rod (measured with a meter stick): 600 +/- 1 mm

Cross-sectional diameter d of the rod (measured with a caliper): 6.1 +/- 0.1 mm

The change in length ∆L after the rod reached its final temperature: 1.04 +/- 0.01 mm

The initial temperature of the rod (the room temperature): 22 +/- 1 ̊C
The final temperature of the rod shown by the thermometer: 93 +/- 1 ̊C

Linear thermal expansion coefficient calculation:

1) Use the experimental values of ∆L, L0, and ∆T (calculate it from the initial and final temperatures of the rod) to calculate the expansion coefficient α.

2) Calculate the uncertainty introduced into the value of α by the uncertainties of ∆L, L0, and ∆T.
3) Which quantity, ∆L, L0, or ∆T, introduces the largest uncertainty into the value of α? Explain.
4) In this experiment, ∆L is measured rather precisely (to 0.01 mm) while the precision of L0 is not as high (1 mm). Why should ∆L be measured to a much greater precision than L0 in this lab?

5) Report your value of α (mean +/- uncertainty, units).

6) Compare the value of α which you have reported in question 5 to the known values of linear thermal expansion coefficients in the OpenStax book (Table 13.2 in Ch.13). Given your measured expansion coefficient, what metal was the rod made of?

7) What is the relative discrepancy between your value in question 5 and the accepted value of α for that metal?

Mechanical implications of thermal expansion:

Under mechanical stress, a metal rod expands or contracts according to the following equation: F/A = Y ∆L/ L0. In this equation, F is the force applied to the rod, A is the cross-section area of the rod, L0 is the initial length, and ∆L is the change in length. The coefficient Y is called the Young’s modulus. It depends on the material the rod is made of (but it is independent of the size or shape of the rod). The ratio F/A is called stress (or tensile stress). It has the same units as pressure (Pa, or N/m2).

8) In your book (Table 5.3 in Ch.5), find the value of Young’s modulus for the material your rod is made of. Using the measured values of ∆L and L0, calculate the stress that would build up in the rod in this experiment if the rod were not allowed to expand freely when heated.

9) Compare the stress you calculated to the atmospheric pressure, Patm= 1.01 ×105 Pa. How many times is the stressyou have just calculated greater than the atmospheric pressure?

10) Using the measured value of the rod’s diameter, calculate the cross-sectional area A of the rod.
11) Use the cross-sectional area to calculate the force that would be needed to keep the rod from expanding in this experiment. Do not forget to indicate the units of the calculated force.
12) Convert your answer for the force to pounds (1 lb = 4.45 N) to get a better appreciation for the magnitude of the force.

13) Given your results in questions 9 and 12, discuss why it is necessary to put thermal expansion joints on bridges and insert U-shaped sections into gas (or oil) carrying pipelines. What other examples of practical implications ofthermal expansion you can think of?

14) How is the behavior of water between 0̊C and 4̊C different from that of the rod used in this lab? Describe thebehavior of a pond as it freezes if water did not behave the way it does (if it kept shrinking when cooled from 4̊C to 0̊C).

Answer 1