Thermal Expansion 2
-Thermal Expansion: Why trains tend to go ‘clack-clack’ offset gaps in the rails to allow for them to expand.
Nathaniel Cooper Ph.D.
September 5, 2018
Name: Nathaniel Cooper Ph.D.
email: Nathaniel.Cooper@sunywcc.edu
Office: Science Rm 354
Lab 25%: Approximately 13 lab reports due every week.
Exams 50%: 5 exams, one during lab. Lowest grade will be dropped. You will get 1 page, front and back of notes.
Final 25%: Comprehensive, 2 pages of notes allowed.
The Lecture section blackboard page will be used for all course material. Check in regularly for announcements and study materials.
Text: Young and Freedman, University Physics vols 1 and 2, 14th Ed.
Temperature: We think of Temperature as an object’s ‘hotness’ or ‘coldness’. More formally, Temperature measures the mean (average) kinetic energy of the atoms/molecules of the object.
Thermometers: The devices we use to measure temperature. Three different styles are used:
Our bodies feel heat, the transfer of energy, not temperature, the average KE.
When two bodies, A and B, are allowed to interact, Heat transfer will be such that The higher temperature object (A) will transfer energy to the lower temperature object, B until they reach the same temperature.
Objects are in thermal equlibrium, if and only if, they are the same temperature.
Insulators slow down the transfer of energy (heat). In the previous slide, A, B, and C must be insulated from their surroundings to get an accurate measurement. They must also be initially insulated from each other.
Conductors allow the transfer of energy (heat) to occur at a higher rate. Replacing the insulators between A, B, and C allow us to measure the objects going to thermal equilibrium with each other.
What types of materials do you think of as good heat insulators?
How about conductors?
Celsius Scale: Global Standard
Fahrenheit Scale: The American System
Kelvin Scale: Nature’s System
\(T_F = 1.8*T_C + 32\)
\(T_C = \frac{T_F - 32}{1.8}\)
\(T_K = T_C +273.15\)
\(T_K = \frac{T_F - 32}{1.8} +273.15\)
\(T_C\) is temperature in Celsius, \(T_F\) is temperature in Fahrenheit, \(T_K\) is temperature in Kelvin
What is -40o F in degrees Celsius?
What is -40o F in Kelvin?
In a constant volume container, if you reduce the temperature of a gas, the pressure the gas exerts on the container wall decreases.
The Kelvin Scale is based on this effect.
\[ \frac{T_2}{T_1} = \frac{p_2}{p_1} \]
The T’s are temperatures in Kelvin. p’s are the pressures in the containers.
The baseline Temperature and Pressure are based on the Triple Point of Water: A pressure/temperature combination where water can exist as a solid. liquid and gas at the same time. T = 0.01o C, p = 610 Pa (0.006 atm).
BY DEFINITION this is 273.16 K
Theoretically, if you reduce temperature low enough, pressure will go to 0 Pa: This is Absolute Zero.
Recall that solids are composed of atoms/molecules that are bonded together.
Temperature is the Average KE of these atoms.
Higher Average KE means more vibrations about these bonds.
Adjacent atoms will push each other out.
Solids will therefore tend to expand as temperature increases.
\[ \Delta L = \alpha L_o \Delta T \]
\(\Delta L\) is the change in length, \(L_o\) is the initial length, \(\Delta T\) is change in temperature, \(\alpha\) that material’s expansion coefficient.
-Thermal Expansion: Why trains tend to go ‘clack-clack’ offset gaps in the rails to allow for them to expand.
This expansion occurs in 3D.
Both solids and liquids will undergo volumetric expansion due to rising temperature.
\[ \Delta V = \beta V_o \Delta T \]
\(\Delta V\) is the change in volume, \(V_o\) is the initial volume, \(\Delta T\) is change in temperature, \(\beta\) that material’s expansion coefficient.
Different materials expand at different rate. As example Ice and Concrete.
As temperature changes the material that expands more per \(\Delta T\) will exert stress on the other material. For ice and concrete, this shatters the concrete creating pot holes in roads.
\[ \frac{F}{A} = -Y \alpha \Delta T \]
Y is the Young’s modulus of the material.