1. Prof. Marlon Flores Sacedon
Thermal Exansion
Prof. Marlon Flores Sacedon
Department of Mathematics and Physics
College of Arts and Sciences
Visayas State University, Visca
Baybay City, Leyte, Phiippines

2. These are examples of Thermal Expansion
Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature, through heat transfer.
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

3. Two Kinds of Thermal Expansion Linear Expansion Volume Expansion

4. Thermal Expansion

5. Thermal Expansion

6. Volume Expansion
Linear Expansion T1 Lo T2
T2>T1
MFS

7. 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)
MFS

8. 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
MFS

9. Relationship between coefficient of volume expansion & coefficient of linear expansion
Recall:

10. 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
MFS

11. 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? Lo
Solution
50 m
Temperature of 20oC
L = ?
Temperature of 35oC
From table, the coefficient of linear expansion
From the formula:
MFS
Ans
Transforming
= m

12. 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.
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
Answer: ∆ 𝑽 𝒐𝒗𝒆𝒓 =𝟐.𝟕 𝒄𝒎 𝟑

13. 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

14. 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

15. eNd