physics 20.3 the kinetic theory of gases

how can the gas laws be explained

by assuming that a gas consists of point molecules moving about at random, continually colliding with the container walls

what causes the pressure of a gas on a containers walls

each impact causes a force on the container, and the force of many impacts causes the pressure of the gas on the container

what type of laws are gas laws

experimental laws, meaning they were devised by experiments and observations

explanation of Boyle's law

the pressure of a gas at constant temperature is increased by reducing its volume because the gas molecules travel less distance between impacts at the walls due to the reduced volume, + so there are more impacts per second = pressure is greater

explanation of the pressure law

the pressure of a gas at constant volume is increased by raising its temperature, which causes the average speed of the molecules to increase, + so the impacts of the molecules on the container walls are harder and more frequent = pressure is raised as a result

the speed of the molecules in an ideal gas

have a continuous spread of speeds - even if the speed of an individual molecule changes, the distribution stays the same, as long as the temperature does not change

the speed of an individual molecule in an ideal gas

changes when it collides with another gas molecule

the root mean square speed of the molecules

c~rms = [(c1^2 + c2^2+ ... + cn^2)/N]^1/2, where (c1^2 + c2^2+ ... + cn^2) represents the speeds of the individual molecules, and where N = the number of molecules in the gas

what happens to the root mean square speed of molecules if the temperature of a gas is raised

the root mean square speed of the molecules increases, as its molecules move faster on average

what happens to the distribution curve of the molecules speeds if the temperature of a gas is raised

the distribution curve becomes flatter and broader because the greater the temperature, the more molecules there are moving at higher speeds

how was the kinetic theory equation derived

by mathematics and theories, instead of by observations and experiments like the gas laws

the kinetic theory equation

pV = 1/3Nm(c~rms)^2

5 assumptions about the molecules in the gas needed in order to derive the kinetic theory equation

they are point molecules + their volume is negligible compared to that of the gas; they don't attract each other; they move about in continual random motion; the collisions they undergo with each other and with the container surface are elastic; each collision with the container surface is of much shorter duration than the time between impacts

elastic collisions

collisions in which there is no overall loss of kinetic energy

why do we need to assume that the molecules don't attract each other in order to derive the kinetic theory equation

if they did, the effect would be to reduced the force of their impacts on the container surface

internal energy of an ideal gas

due only to the kinetic energy of the molecules of the gas

equation for the mean kinetic energy of a molecule of gas

the total kinetic energy of all the molecules/total number of molecules = 1/2m(c~rms)^2

relationship between temperature and mean kinetic energy of a molecule of a gas

the higher the temperature of a gas, the greater the mean kinetic energy of a molecule of the gas

equation for the mean kinetic energy of a molecule of an ideal gas at absolute temperature T

3/2kT, where k = R/NA

equation for the total kinetic energy of one mole

NA x 3/2kT = 3/2RT, (as k = R/NA)

equation for the total kinetic energy of n moles of an ideal gas

3/2nRT

equation for the internal energy of n moles of an ideal gas at temperature T (in kelvins)

internal energy = 3/2nRT