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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].

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Chapter 10

Chapter 10

Temperature and Kinetic Theory


Definitions
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

Internal Energy


Fahrenheit and celsius scales

Use two points to find the equation…

Fahrenheit and Celsius Scales


Fahrenheit celsius and kelvin scales
Fahrenheit, Celsius and Kelvin Scales

  • F = 9/5 C + 32

  • C = 5/9(F – 32)

  • K = C + 273


Ideal gas law
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
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
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
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?


Examples1
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
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
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
Area and Volume Expansion

  • ΔA = 2αA0ΔT Area Expands with Temperature

  • ΔV = 3αV0ΔT Volume Expands with Temperature


Macroscopic vs microscopic ideal gas law
Macroscopic vs Microscopic Ideal Gas Law

Macroscopic

pV = 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
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)


Chapter 10

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 Nmv2rms

N = # of molecules

m = mass of molecule

vrms = average speed of molecule

Kinetic Theory for Monatomic Gases


Chapter 10
Math… the walls of the container.

pV = 1/3 Nmv2rms = NkbT

So ½ mv2rms = 3/2 kbT

Or 3/2 kbT = ½ mv2rms

What does this mean?

Temperature is proportional to average KE!


Example1
Example the walls of the container.

  • Find the average speed (v2rms) 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
Summary- Kinetic Theory for Monatomic Ideal Gas the walls of the container.

Average Kinetic Energy

  • KEav = ½ m vrms2 = 3/2 kbT

    kb = 1.38 X 10 -23 J/K

    Total Internal Energy

  • U = 3/2 NkbT = 3/2 nRT