1. MFS Thermal Expansion Created by: Marlon Flores Sacedon
Physics section, DMPS
June 2010
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2. Two Kinds of Thermal Expansion Linear Expansion Volume Expansion
Most materials expand when their temperature increase.
The decks of bridges need special joints and supports to allow for
expansion.
A completely filled and tightly capped bottle of water cracks when
it is heated
You can loosen a metal jar lid by running hot
water over it. .
These are examples of Thermal Expansion
Two Kinds of Thermal Expansion
Linear Expansion
Volume Expansion
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3. Volume Expansion
Linear Expansion T1 Lo T2
T2>T1
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4. MFS Volume Expansion Linear Expansion T1 Lo L T2 @ T2 T2>T1T1 T1 Lo L T2
@ T2
T2>T1
T2>T1
Where: = coef. of linear expansion (1/K)
L = change in length (m)
L & Lo = final & initial length (m)
T2&T1= final & initial temperature (oC)
Where: = coef. of volume expansion (1/K)
V = change in volume (m3)
V & Vo = final & initial volume (m3)
T2&T1= final & initial temperature (oC)
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5. MFS Coefficients of Linear Expansion Coefficients of Volume Expansion
Material
[K-1 or (Co)-1]
Aluminum
2.4x10-5
Brass
2.0x10-5
Copper
1.7x10-5
Glass
x10-5
Invar
0.09x10-5
Quartz
0.04x10-5
Steel
1.2x10-5
Material
[K-1 or (Co)-1]
Aluminum
7.2x10-5
Brass
6.0x10-5
Copper
Glass
x10-5
Invar
0.27x10-5
Quartz
0.12x10-5
Steel
3.6x10-5
Ethanol
75x10-5
Carbon Disulfide
115x10-5
Glycerine
49x10-5
Mercury
18x10-5
Relationship between coefficient of volume expansion & coefficient of linear expansion
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6. Example 1: A surveyor uses a steel measuring tape that is exactly 50
Example 1: A surveyor uses a steel measuring tape that is exactly m long at a temperature of 20 oC. What is its length on a hot summer day when the temperature is 35 oC?
Answer: m Lo
Solution
50 m
Temperature of 20oC
L = ?
Temperature of 35oC
From table, the coefficient of linear expansion
From the formula:
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Ans
Transforming
= m

7. Example 2: The surveyor uses the measuring tape (in Example 1) to measure a distance when the temperature is 35 oC; the value that she reads off the tape is m. What is the actual distance?
Answer: m
Solution
Lo = 50 m
Temperature of 20oC
L = m
Temperature of 35oC
Let: x = actual T=35 oC
Ans

8. Example 3: A glass flask with volume 200 cm3 is filled to the brim with mercury at 20 oC. How much mercury overflows when the temperature of the system is raised to 100 oC? The coefficient of linear expansion of the glass is 0.40x10-5 K-1.
Answer: 2.7 cm3
Solution
Mercury overflows ( Vover)
Mercury, expanded volume( VHg)
Glass flask, expanded volume ( Vglass)
Mercury column
Glass flask
From table:
Glass flask filled w/ mercury
@ T1=20oC
@ T2=100oC

9. Seat Work1: The Humber Bridge in England has the world’s longest single span, 1410m in length. Calculate the change in length of steel deck of the span when the temperature increases from -5.0oC to 18.0oC.
Answer: 0.39 m
Seat Work2: A metal rod is cm long at 20.0oC and cm long at 45.0oC. Calculate the average coefficient of linear expansion of the rod for this temperature range.
Answer: 2.3x10-5 (Co)-1
Seat Work3: A glass flask whose volume is cm3 at 0.0oC is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0oC, 8.95 cm3 of mercury overflow. If the coefficient of volume expansion of mercury is 18.0x10-5 K-1, compute the coefficient of volume expansion of the glass.
Answer: 1.7x10-5 (Co)-1

10. Assignment
1) A Pendulum shaft of a clock is made of brass. What is the fractional change in length of the shaft when it is cooled from 19.50oC to 5.00oC?
Answer: -2.9x10-4
2) An underground tank with a capacity of 1700L (1.70m3) is filled with ethanol that has an initial temperature of 19.0oC. After the ethanol has cooled off to the temperature of the tank and ground, which is 10.0oC, how much air space will there be above the ethanol in the tank? (Assume that the volume of the tank doesn’t change.)
Answer: 2.3x10-5 (Co)-1
3) A metal rod that is 30.0 cm long expands by cm when its temperature is raised from 0oC to 100oC. A rod of a different metal and of the same length expands by cm for the same rise in temperature. A third rod, also 30.0 cm long is made up of pieces of each of the above metals placed end-to-end and expands cm between 0oC and 100oC. Find the length of each portion of the composite bar.
Answer: 23.0cm, 7.0cm

11. Thermal Stress (thermal stress) so A F Tensile Stress F Lo Where:
F = Tensile force, (N)
A = cross-section area, (m2)
Y = Young’s Modulus, (Pa or N/m2)
= coef. of linear expansion, (K-1)
= change in tempersture, (K)
Tensile Strain

12. Approximate Young’s Modulus
Substance
Young’s Modulus, Y
(Pa)
Aluminum
7.0x1010
Brass
9.0x1010
Copper
11x1010
Crown glass
6.0x1010
Iron
21x1010
Lead
1.6x1010
Nickel
Steel
20x1010

13. Example 1: An aluminum cylinder 10 cm long, with a cross-section area of 20 cm3, is to be used as a spacer between two steel walls. At 17.2 oC it just slips in between the walls. When it warms to 22.3oC, calculate the stress in the cylinder and the total force it exerts on each wall, assuming that the walls are perfectly rigid and a constant distance apart.
Answer: -8.6x106 and -1.7x104N
F = 0
Area A=20cm3
Lo=10cm
@ T1=17.2 oC
F > 0
Stress is - 8.6x106 Pa
Negative sign indicates compression
Lo=10cm
@ T1=22.3 oC
F = -1.7x104 N (compression)

14. Assignment: a) A wire that is 1
Assignment: a) A wire that is 1.50 m long at 20oC is found to increase in length by 1.9 cm when warmed to 420oC. Compute its average coefficient of linear expansion for this temperature range. b) The wire is stretched just taut (zero tension) at 420oC. Find the stress in the wire if it is cooled to 20oC without being allowed to contact. Young’s modulus for the wire is 20.x1011 Pa.
Answer: a) 3.2x10-5 (Co)-1; b)2.5x109 Pa
1.50 m
@ 20oC
0.019 m
@ 420oC
Ans
1.519 m
@ 420oC
1.519 m
F>0
@ 20oC

15. Assignment
1) A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120oC to 10oC?
Answer: 4.0x104 N
2) Steel train rails are laid in 12.0 m-long segments placed end-to-end. The rails are laid on a winter day when their temperature is -2.0oC. a) How much space must be left between adjacent rails if they are to just touch on a summer day when their temperature is 33.0oC? b) If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is 33.0oC?
Answer: a) 5.0x10-3 m; b) 8.4x107 Pa