1. Thermal Expansion of Solids/liquids
Questions? (Sound)
February Roadmap
Temperature Scales
Properties of Materials with Temperature
Thermal Expansion of solids/liquids
Ideal Gas Law for gases
Phase change
Examples

2. February Roadmap Chapter 13 – Temperature Chapter 14 – Heat
Temperature scales
Thermal Expansion of solids and liquids
Ideal Gas Law for gases
Phases of materials
Chapter 14 – Heat
Specific Heat
Latent Heat
Heat Transport Mechanisms
Chapter 15 – Thermodynamics
First Law of Thermodynamics - Energy
Thermodynamic Cycles - Heat Engines
Second Law of Thermodynamics - Entropy

3. Thermodynamics Perspective
𝑇ℎ𝑒𝑟𝑚𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠= 𝑃ℎ𝑦𝑠𝑖𝑐𝑠 103 ∗ 6.02 ∗ (𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙 𝑎𝑣𝑒𝑟𝑎𝑔𝑖𝑛𝑔)

4. Temperature Scales 1.0 Dorm room thermostat 2 1 3
Just landed from Planet X, need to learn “temperature”
Dorm room thermostat
(1= cool, 2 = pleasant, 3 = hot) 2 1 3
pleasant
hot
cold

5. Temperature Scales 2.0 That’s the Celsius Scale! 20 10 30 oC
Tired of fractions/decimals, so multiply by 10 (add zero)
That’s the Celsius Scale!
(10 = cool, 20 = pleasant, 30 = hot) 20 10 30
pleasant
hot
cold oC

6. Temperature Scales 2.0

7. Temperature Scales 3.0 Below 0 = freezing, above 0 = raining 20 10 30
Including winter temperatures…
Below 0 = freezing, above 0 = raining
(Lancaster’s -5 to 5 this time of year) 20 10 30
freeze
snow
rain oC
-10

8. Typical Lancaster - C° Bitter Jan. cold (a week ago) -12
Typical winter to 5
Typical March 7 to 12
April/October hiking 15
Perfect May Day 21
A bit Warm 28
Hot
Brutal July Hot 38

9. Celsius vs. Kelvin Degree sizes same!
Kelvin = Celsius with zero shifted to absolute zero.
𝑇 𝐾 =𝑇 𝐶
May use Celsius when only relative changes important.
Thermal Expansion
Specific and Latent Heat problems
Thermal Conduction
Must use Kelvin when absolute temperature important.
Ideal Gas Law
Kinetic Theory
Thermal Radiation
First and Second Law Thermodynamics
Similar to Gauge vs. Absolute Pressure

10. Thermal Expansion in Solids/Liquids
Thermal Expansion of 1-D solid
∆𝐿=𝛼 𝐿 𝑜 ∆𝑇
Lo – base length
ΔL – length change
ΔT – temperature change
α - material property
Similar to stress/strain
∆𝐿= 1 𝐸 𝐿 𝑜 𝐹 𝐴
Lo – base length
ΔL – length change
F/A – stress
1/E - material property
Total expanded length
𝐿= 𝐿 𝑜 1+𝛼∆𝑇

11. Coefficients of Thermal Expansion

12. Example 13-1 - Expansion of Bridge Joint
Temperature change to -30C
∆𝑇= −30𝐶 − 20𝐶 =−50𝐶
Length change to -30C
∆𝐿=𝛼 𝐿 𝑜 ∆𝑇
=(12∙ 10 −6 𝐶)(200 𝑚)(−50𝐶)
=−12 𝑐𝑚
Temperature change to 40C
∆𝑇= 40𝐶 − 20𝐶 =20𝐶
Length change to 40C
=(12∙ 10 −6 𝐶)(200 𝑚)(20𝐶)
=+4.8 𝑐𝑚
Total length change 16.8 cm

13. Thermal Expansion failure
A "mechanical failure" on the Nipigon River Bridge has closed the Trans-Canada Highway, severing the only road between Eastern and Western Canada.

14. Example 13-4 – Expansion of Ring
Ring expands along circumference
∆𝐿=𝛼 𝐿 𝑜 ∆𝑇
Diameter proportional to
to circumference
𝑑= 𝐿 𝑜 𝜋
Diameter change proportional to
to circumference change
∆𝑑= ∆𝐿 𝑜 𝜋 = 𝛼 𝐿 𝑜 ∆𝑇 𝜋 =𝛼 𝑑 𝑜 ∆𝑇
Ring get larger

15. Example 13-5 - Ring on a Rod ∆𝑑= ∆𝐿 𝑜 𝜋 = 𝛼 𝐿 𝑜 ∆𝑇 𝜋 =𝛼 𝑑 𝑜 ∆𝑇
Ring must expand to match rod = cm
Must expand another cm to clear cm cm = cm
Thermal expansion of diameter
∆𝑑= ∆𝐿 𝑜 𝜋 = 𝛼 𝐿 𝑜 ∆𝑇 𝜋 =𝛼 𝑑 𝑜 ∆𝑇
0.033 𝑐𝑚= 12∙ 10 −6 𝐶 cm ∆𝑇
∆𝑇=430 𝐶
Final temperature 20 C C = 450 C

16. Linear vs. Volume Thermal Expansion
Linear Thermal Expansion in 1-D (solid)
∆𝐿=𝛼 𝐿 𝑜 ∆𝑇
Lo – base length
ΔL – length change
ΔT – temperature change
α - material property
Volume Thermal Expansion in 3-D (liquids)
∆𝑉=𝛽 𝑉 𝑜 ∆𝑇
Vo – base length
ΔV – length change
β - material property

17. Volume Thermal Expansion
Volume expansion of gasoline ∆𝑉=𝛽 𝑉 𝑜 ∆𝑇 ∆𝑉=(950 ∙ 10 −6 𝐶)(70 𝐿)(40𝐶−20𝐶) =1.3 𝐿 Volume expansion of steel tank ∆𝑉=(36 ∙ 10 −6 𝐶)(70 𝐿)(40𝐶−20𝐶) =0.5 𝐿 Difference spills out 1.3 L – 0.05 L = 1.25 L