Our model of an ideal gas consists of a number of particles moving with a given energy, as explained before. The internal energy U of a system is defined as the sum of the energies of its individual particles, while the temperature T is related to the average energy per particle.
Collisions are the mechanism that allows random exchanges of energy between the particles. All the degrees of freedom of the molecules of the gas have to be considered concerning the energy exchanges. For the simplest case of a monoatomic gas all the energy is translational kinetic energy, which is the one directly related to the temperature, as we shall see below.
Microscopic interpretation of temperature
The simulation shows an ideal gas with 150 particles moving randomly. The values of the total energy and the temperature are shown in two different windows, and can be changed with the arrows. In order to look at the microscopic effect of temperature, without changing the number of particles:
Select one of the following options:
Searching for the relation between P and T.
Looking at the results obtained in the experience choose one of the following options:
|Check your conclusions by clicking here.|
From this experience and that
one in Section 2. PRESSURE
led to the conclusion that the following relationship holds for an
gas made up of N
PV/T = constant
In a more quantitative way the
experimentally found relationship reads
PV = NkT
where P is the pressure, V the volume, N the number of particles, k the Boltzmann's constant and T the temperature.
The pressure on the walls
arises from the change in momentum of the
particles colliding with the walls. A particle with x-component Px of
before the collision with the wall emerges from the collision with
sign in this component, so the change in momentum is
The particles that collide with
the wall within a given time interval
dt are those placed at a distance from the wall less than
Therefore, the total change of
momentum of the gas is
The force exerted by the gas on
the wall is obtained as the change in
momentum per unit time, and divided by the area of the wall gives the
of the pressure. Taking into account that the x-component of the
is not the same for all the particles in the gas, the average value
where the experimental relationship between P, V and T has been employed. From this expression we deduce that the average kinetic energy per particle corresponding to motion along the X-axis is kT/2. As all directions in space are equivalent, the energy corresponding to motion along the Y- and Z-axis must be the same, and finally we arrÙve at the conclusion that
Internal energy and Temperature.
Looking at the results obtained in this experience, carried out with a monoatomic gas, choose one of the following options
|6.First Law||7.First Law||8.Entropy||9.Velocity Distribution||10.Specific Heat|