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Chapter 13
Temperature and Kinetic
Theory
13-1 Atomic Theory of Matter
- Atomic mass unit (u)
- This unit is defined so carbon-12 has a mass of exactly 12.0000 u. Expressed in kilograms: Brownian motion is the result of collisions with individual water molecules.
13-1 Atomic Theory of Matter
- atomic nature of matter
- Democritus - atom
- Brownian motion (Robert Brown, 1827)
- the result of collisions with individual water molecules
- quantified by Einstein (1905)
13-1 Atomic Theory of Matter
On a microscopic scale, the arrangements of molecules in solids (a), liquids (b), and gases (c) are quite different.
13-2 Temperature and Thermometers
Temperature is a measure of how hot or cold something is. Most materials expand when heated.
13-2 Temperature and Thermometers
Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature. Early thermometers:
13-2 Temperature and Thermometers
Common thermometers used today include the liquid-in-glass type and the bimetallic strip.
13-2 Temperature and Thermometers
- Most common temp scales: Fahrenheit and Celsius
- Defined by phase change of water at atmospheric pressure
- freezing point of water
- boiling point of water
- 100°C or 212°F. Chapter 13: Problem 3(a)
- Room temperature is 680 F. What is this in
Celsius?
13-3 Thermal Equilibrium and the Zeroth
Law of Thermodynamics
- Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.
- zeroth law of thermodynamics: if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other.
13-4 Thermal Expansion
Linear expansion occurs when an object is heated. (13-1b) Here, α is the coefficient of linear expansion. Ch 13: Problem 7
- A concrete highway is built of slabs 12 m
long (20^0 C). How wide should the
expansion cracks between the slabs be (at
200 C) to prevent buckling if the range of
temperature is -30^0 C and +50^0 C?
13-7 The Ideal Gas Law
A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular mass of the substance: 1 mol H 2 has a mass of 2 g 1 mol Ne has a mass of 20 g 1 mol CO 2 has a mass of 44 g The number of moles in a certain mass of material:
13-7 The Ideal Gas Law
ideal gas law: (13-3) where n is the number of moles and R is the universal gas constant.
13-8 Problem Solving with the Ideal Gas Law
Useful facts and definitions:
- Standard temperature and pressure (STP)
- Volume of 1 mol of an ideal gas is 22.4 L
- If the amount of gas does not change:
- Always measure T in kelvins
- P must be the absolute pressure Ch 13: Problem 29
- If 3.00 m^3 of a gas initially at STP is placed
under a pressure of 3.20 atm, the
temperature of the gas rises to 38.0^0 C.
What is the volume?
13-9 Ideal Gas Law in Terms of Molecules:
Avogadro’s Number
Avogadro’s number: the number of molecules in one mole The number of molecules in a gas is the number of moles times Avogadro’s number:
13-9 Ideal Gas Law in Terms of Molecules:
Avogadro’s Number
Therefore we can write: where k is called Boltzmann’s constant. (13-4)
Ch13: Problem 42
- How many moles of water are there is
1.000 L? How many molecules?
13-10 Kinetic Theory and the Molecular
Interpretation of Temperature
Assumptions of kinetic theory:
- large number of molecules, moving in random directions with a variety of speeds
- molecules are far apart, on average
- molecules obey laws of classical mechanics and interact only when colliding
- collisions are perfectly elastic
13-10 Kinetic Theory and the Molecular
Interpretation of Temperature
(13-8) The average translational kinetic energy of the molecules in an ideal gas is directly proportional to the temperature of the gas.
13-10 Kinetic Theory and the Molecular
Interpretation of Temperature
We can invert this to find the average speed of molecules in a gas as a function of temperature: (13-9) Ch 13: Problem 47
- Calculate the rms speed of helium atoms
near the surface of the Sun at a
temperature of about 6000 K.
