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

A steel rod without constrain has a length of 200 mm and
diameter of 20 mm at a temperature of 25oC. If the rod
is heated uniformly to 125oC, what will be the length
and diameter (accurate to 1/100 mm). What will be the stress at
125oC? The linear coefficient of thermal expansion of
steel is 12.5x10-6 m/m/C.

A rod has a square cross section of (5 x 5) mm. length of the
rod is 120 cm. The allowable stress is 400 MPa. After applying the
load (F), square section changes to (4.95 x 4.95) mm.
1. What is the type of the load (F), is it tension or
compression?
2. What is the longitudinal strain in steel rod?
3. What is the modulus of elasticity of the material of the
rod?
4. What is the value of...

a.) An aluminum rod has an initial length of Lo = 670
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value should the temperature be raised such that the rod would
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expansion of aluminum is 23.80x10^-6 Co.
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Q.1. Measurement of four lengths is given in
Table.
Measured Length ( m )
Temperature ( C )
Tension ( N )
1
29.899
18.0
178
2
29.901
18.0
178
3
29.882
18.1
178
4
29.950
17.9
178
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pr.1 The Observations were made from station P to signal at
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between Pand Qis 12.5 km and diameter of signal at station Q was 20
cm. The sun rays make an angle
of 50° with line PQ. Calculate the phase correction if observations
were made:on the bright portion,on the bright line.. ,A base line
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ata pull of 100 N. The measured length of...

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D-Calculate the atomic packing factor for FCC and BCC
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E-Compute the elongation due to thermal expansion of given
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Evf
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What is the change in length of a metal rod with an original
length of 4 m, a coefficient of thermal expansion of 0.00002/ ° C,
and a temperature change of 30° C?
1.
2.4 mm
2.
12 mm
3.
1.2 mm
4.
24 mm
Determine the number of electrons passing through a point in the
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a.
3 * 1016 electrons
b.
none of these
c.
4,800 electrons
d.
1.6...

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