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Deriving the kinetic theory of gas, including assumptions. Some questions to use the theory to explain certain phenomena.
What are the assumptions made in the kinetic theory model of an ideal gas?
The particles are point masses (their volume is negligible compared to that of the gas)
The particles do not interact with each other except for during collisions (there are no forces between particles)
Particles are in random motion
The collisions between particles or particles and the wall are elastic (kinetic energy is conserved)
The duration of collisions is negligible compared to the time between collisions
all particles are identical (extra)
What is the internal energy of an ideal gas?
The total kinetic energy of the particles (in the gas)
Why is the internal energy of an ideal gas equal to the total kinetic energy of the particles?
There are no forces between particles, and particles are not affected by gravity. Therefore there is no potential energy?
What is internal energy (of an gas)
The sum of all the kinetic and potential energies of the particles of a gas.
What is the Crms?
The root mean square speed of (all) particles in a gas.
Root of the mean of the squares.
Show how to find Crms in the derivation of kinetic theory of a gas.
Do all particles in a gas travel at the same speed?
No, they travel at a range of speeds (that are similar).
Explain in terms of the kinetic theory why the pressure of the gas in the cylinder falls when gas is removed from the cylinder.
p = F/A, particles exert forces on the wall
Pressure is a result of particles colliding with the walls of the container (and each other)
When gas is removed, there are fewer particles in the container resulting in fewer collisions per second
mean square speed is constant
Volume and mass are constant
speed squared is constant as temperature is constant
pressure is directly proportional to the number of particles (N).
Use the kinetic theory of gases to explain why the pressure exerted by an ideal gas increases when it is heated at a constant volume.
Increasing temperature increases the average velocity of particles, resulting in more collision per second
It also results in more momentum change per collision
p = F/A, force increases because of increased momentum change per second
Which results in a greater pressure.
Use the kinetic theory of gases to explain why the volume occupied by an ideal gas increases when it is heated at a constant pressure.
Increasing temperature increases the average velocity of particles, which increases the change in momentum per collision
The volume increases resulting in fewer collision per second (to maintain the same pressure).
How is the absolute zero of temperature interpreted in terms of the kinetic energy of particles in an ideal gas?
The temperature at which the continuous random motion of particles stops. (Ek = 0 as Ek = (mCrms²/2) so Crms² = 0)
