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College Physics 2e

# Section Summary

College Physics 2eSection Summary

## 13.1Temperature

• Temperature is the quantity measured by a thermometer.
• Temperature is related to the average kinetic energy of atoms and molecules in a system.
• Absolute zero is the temperature at which there is no molecular motion.
• There are three main temperature scales: Celsius, Fahrenheit, and Kelvin.
• Temperatures on one scale can be converted to temperatures on another scale using the following equations:
$T º F = 9 5 T º C + 32 T º F = 9 5 T º C + 32$
$T º C = 5 9 T º F − 32 T º C = 5 9 T º F − 32$
$T K = T º C + 273 . 15 T K = T º C + 273 . 15$
$T º C = T K − 273 . 15 T º C = T K − 273 . 15$
• Systems are in thermal equilibrium when they have the same temperature.
• Thermal equilibrium occurs when two bodies are in contact with each other and can freely exchange energy.
• The zeroth law of thermodynamics states that when two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C.

## 13.2Thermal Expansion of Solids and Liquids

• Thermal expansion is the increase, or decrease, of the size (length, area, or volume) of a body due to a change in temperature.
• Thermal expansion is large for gases, and relatively small, but not negligible, for liquids and solids.
• Linear thermal expansion is
$ΔL=αLΔT,ΔL=αLΔT,$
where $ΔLΔL$ is the change in length $LL$, $ΔTΔT$ is the change in temperature, and $αα$ is the coefficient of linear expansion, which varies slightly with temperature.
• The change in area due to thermal expansion is
$ΔA=2αAΔT,ΔA=2αAΔT,$
where $ΔAΔA$ is the change in area.
• The change in volume due to thermal expansion is
$ΔV=βVΔT,ΔV=βVΔT,$
where $ββ$ is the coefficient of volume expansion and $β≈3αβ≈3α$. Thermal stress is created when thermal expansion is constrained.

## 13.3The Ideal Gas Law

• The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
• The ideal gas law can be written in terms of the number of molecules of gas:
$PV=NkT,PV=NkT,$
where $PP$ is pressure, $VV$ is volume, $TT$ is temperature, $NN$ is number of molecules, and $kk$ is the Boltzmann constant
$k=1.38×10–23 J/K.k=1.38×10–23 J/K.$
• A mole is the number of atoms in a 12-g sample of carbon-12.
• The number of molecules in a mole is called Avogadro’s number $NANA$,
$NA=6.02×1023mol−1.NA=6.02×1023mol−1.$
• A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
• The ideal gas law can also be written and solved in terms of the number of moles of gas:
$PV=nRT,PV=nRT,$
where $nn$ is number of moles and $RR$ is the universal gas constant,
$R=8.31J/mol⋅K.R=8.31J/mol⋅K.$
• The ideal gas law is generally valid at temperatures well above the boiling temperature.

## 13.4Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

• Kinetic theory is the atomistic description of gases as well as liquids and solids.
• Kinetic theory models the properties of matter in terms of continuous random motion of atoms and molecules.
• The ideal gas law can also be expressed as
$PV = 1 3 Nm v 2 ¯ , PV = 1 3 Nm v 2 ¯ ,$
where $PP$ is the pressure (average force per unit area), $VV$ is the volume of gas in the container, $NN$ is the number of molecules in the container, $mm$ is the mass of a molecule, and $v 2 ¯ v 2 ¯$ is the average of the molecular speed squared.
• Thermal energy is defined to be the average translational kinetic energy $KE¯KE¯$ of an atom or molecule.
• The temperature of gases is proportional to the average translational kinetic energy of atoms and molecules.
$KE ¯ = 1 2 m v 2 ¯ = 3 2 kT KE ¯ = 1 2 m v 2 ¯ = 3 2 kT$

or

$v 2 ¯ = v rms = 3 kT m . v 2 ¯ = v rms = 3 kT m .$
• The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.

## 13.5Phase Changes

• Most substances have three distinct phases: gas, liquid, and solid.
• Phase changes among the various phases of matter depend on temperature and pressure.
• The existence of the three phases with respect to pressure and temperature can be described in a phase diagram.
• Two phases coexist (i.e., they are in thermal equilibrium) at a set of pressures and temperatures. These are described as a line on a phase diagram.
• The three phases coexist at a single pressure and temperature. This is known as the triple point and is described by a single point on a phase diagram.
• A gas at a temperature below its boiling point is called a vapor.
• Vapor pressure is the pressure at which a gas coexists with its solid or liquid phase.
• Partial pressure is the pressure a gas would create if it existed alone.
• Dalton’s law states that the total pressure is the sum of the partial pressures of all of the gases present.

## 13.6Humidity, Evaporation, and Boiling

• Relative humidity is the fraction of water vapor in a gas compared to the saturation value.
• The saturation vapor density can be determined from the vapor pressure for a given temperature.
• Percent relative humidity is defined to be
$percent relative humidity = vapor density saturation vapor density × 100 . percent relative humidity = vapor density saturation vapor density × 100 .$
• The dew point is the temperature at which air reaches 100% relative humidity.
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