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# Kinetic Theory of Gases - PowerPoint PPT Presentation

Kinetic Theory of Gases. Physics 202 Professor Lee Carkner Lecture 13. What is a Gas?. But where do pressure and temperature come from? A gas is made up of molecules (or atoms) The pressure is a measure of the force the molecules exert when bouncing off a surface

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Physics 202

Professor Lee Carkner

Lecture 13

• But where do pressure and temperature come from?

• A gas is made up of molecules (or atoms)

• The pressure is a measure of the force the molecules exert when bouncing off a surface

• We need to know something about the microscopic properties of a gas to understand its behavior

• A gas is composed of molecules

• m =

• N =

• When thinking about molecules it sometimes is helpful to use the mole

1 mol = 6.02 X 1023 molecules

• 6.02 x 1023 is called Avogadro’s number (NA)

• M =

M = mNA

• A mole of any gas occupies about the same volume

• Specifically, 1 mole of any gas held at constant temperature and constant volume will have almost the same pressure

• Gases that obey this relation are called ideal gases

• A fairly good approximation to real gases

• The temperature, pressure and volume of an ideal gas is given by:

pV = nRT

• Where:

• R is the gas constant 8.31 J/mol K

• V in cubic meters

p=nRT (1/V)

• If we hold the temperature constant in the work equation:

W = nRT ln(Vf/Vi)

• Work for ideal gas in isothermal process

• From the ideal gas law we can get an expression for the temperature

• For an isothermal process temperature is constant so:

• If P goes up, V must go down

• Lines of constant temperature

• One distinct line for each temperature

W=0

W = pdV = p(Vf-Vi)

W = pDV

• For situations where T, V or P are not constant, we must solve the integral

• The above equations are not universal

• The molecules bounce around inside a box and exert a pressure on the walls via collisions

• The pressure is a force and so is related to velocity by Newton’s second law F=d(mv)/dt

• The rate of momentum transfer depends on volume

• The final result is:

p = (nMv2rms)/(3V)

• Where M is the molar mass (mass of 1 mole)

• There is a range of velocities given by the Maxwellian velocity distribution

• We take as a typical value the root-mean-squared velocity (vrms)

• We can find an expression for vrms from the pressure and ideal gas equations

vrms = (3RT/M)½

• For a given type of gas, velocity depends only on temperature

Maxwell’sDistribution

• Using the rms speed yields:

Kave = ½mvrms2

Kave = (3/2)kT

• Where k = (R/NA) = 1.38 X 10-23 J/K and is called the Boltzmann constant

• Temperature is a measure of the average kinetic energy of a gas

• The vrms of protons is not large enough for them to combine in hydrogen fusion

• There are enough protons in the high-speed tail of the distribution for fusion to occur