Chapter 20 The kinetic Theory of Gases. The mole is one of the seven SI base units and is defined as follows:. One mole is the number of atoms in a 12 g sample of carbon – 12. The number of moles n is. 20-2 Avogadro’s Number. At low enough densities,all real gases tend to obey the relation.
One mole is the number of atoms in a 12 g sample of carbon – 12.
The number of moles n is
The gas constant R
The Boltzmann constant k
On a p-v diagram,an relationisotherm is a curve that connects point that have the same temperature.
If the volume of the gas is constant relation
If the pressure of the gas is constant
Sample Problem 20-1
Sample Problem 20-2 relation
The average rate at which momentum is delivered to the shaded wall by this single molecule is
The pressure is
Combining Eq.20-21 with the ideal gas law leads to
Its average translational kinetic energy over the time that we watch it is
20-5 Translational Kinetic Energy
Something unexpected: axis:
At a given temperature T, all ideal gas molecules – no matter what their mass – have the same average translational kinetic energy ,namely , kT .When we measure the temperature of a gas ,we are also measuring the average translational kinetic energy of its molecules.
The value of this total area is unity
The fraction (frac) of molecules with speed in an interval of,say, v1to v2is:
The average speed is: axis:
The average of the square of the speed is
The root – mean – square speed is :
Internal Energy E axis:int
The internal energy Eint of the sample is
The internal energy Eint of an ideal gas is a function of the gas temperature only;it does not depend on any other variable.
is a constant called the molar specific heat at constant volume.
A change in the internal energy Eint of a confined ideal gas depends on the change in the gas temperature only;it does not depend on what type of process process the change in the temperature.
The equipartition of energy pressure.
Every kind of molecule has a certain number f of degrees of freedom, which are independent ways in which the molecule can store energy.Each such degree of freedom has associated with it—on average —an energy of per molecule (or per mole) .
20-10 A Hint of Quantum Theory
The relation between the pressure and the volume during such an adiabatic process is
the ratio of the molar specific heats for
Proof of Eq. 20-53 an adiabatic process is
The first law of thermodynamics can then be written as
From the ideal gas law,we have an adiabatic process is
The initial and final points on a p-v diagram must be on the same isotherm,and instead of Eq.20-56
(a) an adiabatic process is
The number of moles n is
The Boltzmann constant k an adiabatic process is
Work in an Isothermal Volume Change
Pressure,Temperature,and Molecular Speed
Temperature and Kinetic Energy an adiabatic process is
Mean Free Path
Maxwell Speed Distribution
Molar Specific Heats an adiabatic process is
Degrees of Freedom and Cv an adiabatic process is