Chapter 10 Temperature and Kinetic Theory. Definitions Temperature – a measure of the average...
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Transcript of Chapter 10 Temperature and Kinetic Theory. Definitions Temperature – a measure of the average...
Chapter 10
Temperature and Kinetic Theory
Definitions Temperature – a measure of the average
kinetic energy of the the molecules making up a substance, measured in [C] or [F] or [K].
Internal Energy (thermal energy) the combined kinetic and potential energy of the molecules of a substance measured in [Joules].
Heat – the transfer of thermal energy measured in [Joules].
Internal Energy Kinetic energy –
when molecules are in motion
Potential energy – when molecules have stored energy
Fahrenheit and Celsius Scales
Use two points to find the equation…
Fahrenheit, Celsius and Kelvin Scales
F = 9/5 C + 32
C = 5/9(F – 32)
K = C + 273
Ideal Gas Law PV = nRT
P = Pressure V = Volume n = number of moles R = univ. gas constant (8.31 J/mol ºK) T = Temperature in Kelvin
Things to Know A mole of a substance is a quantity
containing 6.02 X 1023 molecules Standard Temperature and Pressure
means p = 1 atm = 1.01 X 105 Pa, T = 0ºC = 273 K
Formula weight in Grams = 1 mole Must use Kelvin for temperature!
Special Cases of Ideal Gas Law
If the number of molecules (mass) doesn’t change:
Constant Temperature, then p1V1 = p2V2
Constant Pressure , then V1/T1 = V2/T2
Constant Volume, then p1/T1 = p2/t2
Examples A low density gas in a rigid
container is initially at 20ºC and a particular pressure, p1. If the gas is heated to 60ºC, by what factor does pressure change?
Examples The weather report gives the day’s
high temperature as 10ºC and predicts the next day’s high temperature as 20ºC. A father tells his son that this means it will be twice as warm tomorrow, but the son says it does not mean that. Do you agree with the father or the son?
Thermal Expansion Solids and liquids expand or contract
with changes in temperature.
Space between molecules becomes greater or less as temperature changes.
ΔL = αL0ΔT ; L0= original length
α = thermal coefficient of linear expansion
Example
A steel beam is 5.0 m long at 20ºC. On a hot day, the temperature rises to 40ºC. What is the change in the beam’s length? α = 12 X 10-6 C-1
Area and Volume Expansion
ΔA = 2αA0ΔT Area Expands with Temperature
ΔV = 3αV0ΔT Volume Expands with Temperature
Macroscopic vs Microscopic Ideal Gas Law
MacroscopicpV = nRT R = 8.31 J/mol K
n = # of moles Microscopic
pV = NkbT kb = 1.38 X 10-23 J/K
N = # of molecules
Kinetic Theory for Monatomic Gases
Monatomic – single atom gases. Diatomic – molecules contain 2 atoms.
Monatomic gases are easy to study because atoms move without rotation or vibration
Monatomic gases obey the laws of mechanics (recall for elastic collisions we apply Conservation of Momentum and Conservation of Energy)
Molecules (atoms)
undergo perfectly elastic collisions with the walls of the container.
We assume molecules are separated by large enough distances so that molecular collisions can be neglected.
Then… pV = 1/3 Nmv2
rms
N = # of molecules
m = mass of molecule
vrms = average speed of molecule
Kinetic Theory for Monatomic Gases
Math…pV = 1/3 Nmv2
rms = NkbT
So ½ mv2rms = 3/2 kbT
Or 3/2 kbT = ½ mv2rms
What does this mean?Temperature is proportional to average KE!
Example Find the average speed (v2
rms) of a Helium atom in a 20ºC balloon at room temperature. Assume mHe = 6.65 X 10-27 kg
Summary- Kinetic Theory for Monatomic Ideal Gas
Average Kinetic Energy KEav = ½ m vrms
2 = 3/2 kbT
kb = 1.38 X 10 -23 J/K
Total Internal Energy U = 3/2 NkbT = 3/2 nRT