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

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

Thermodynamics Perspective 𝑇ℎ𝑒𝑟𝑚𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠= 𝑃ℎ𝑦𝑠𝑖𝑐𝑠 103 ∗ 6.02 ∗ 10 23 + (𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙 𝑎𝑣𝑒𝑟𝑎𝑔𝑖𝑛𝑔) http://en.wikipedia.org/wiki/Statistical_mechanics

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

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

Temperature Scales 2.0

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

Typical Lancaster - C° Bitter Jan. cold (a week ago) -12 Typical winter -5 to 5 Typical March 7 to 12 April/October hiking 15 Perfect May Day 21 A bit Warm 28 Hot 32 Brutal July Hot 38

Celsius vs. Kelvin Degree sizes same! Kelvin = Celsius with zero shifted to absolute zero. 𝑇 𝐾 =𝑇 𝐶 +273.15 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

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

Coefficients of Thermal Expansion

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

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. http://www.thestar.com/news/gta/2016/01/10/bridge-closure-cuts-off-trans-canada-traffic-forces-us-detour.html

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

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 6.445 - 6.420 = 0.025 cm Must expand another 0.008 cm to clear 0.025 cm + 0.008 cm = 0.033 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 6.420 cm ∆𝑇 ∆𝑇=430 𝐶 Final temperature 20 C + 430 C = 450 C

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

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