Kinetic Theory

molecular motion would theoretically stop. In physics and many scientific circles, it’s the Kelvin scale that is used.

For the calculation from Fahrenheit to Celsius, you take nine-fifths of the difference between the Fahrenheit degrees and 32. The difference between Kelvin and Celsius is 273.15 degrees, with the Celsius scale just being a version of the Kelvin scale. Standard temperature is said to be 25 degrees Celsius, which is approximately “room temperature”.

You should know that absolute zero on the Kelvin scale isn’t the lowest possible temperature recorded or possible. The coldest temperature on Earth recorded has been 183 degrees Kelvin or -89 degrees Celsius. The lowest temperature recorded has been 1 x 10-10 degrees Kelvin, which is far below the level of absolute zero. The coldest place outside Earth in the known universe outside of a laboratory is 1-degree Kelvin in the Boomerang Nebula. The highest known temperature in experimental science is in the range of 1012 degrees Kelvin. In the known universe, the temperature of the interior of a neutron star is 109 degrees Kelvin.

You need to recognize that thermometers take their own temperature and not necessarily the temperature of their environment. There needs to be thermal contact between the thing being measured and the thermometer so that there is thermal equilibrium. Time must pass before this can truly happen as there needs to be transfer of heat. If two systems are in thermal equilibrium and a third system is in equilibrium with a third system, all three systems are in equilibrium. The Zeroth law of thermodynamics indicates that this is true.

KINETIC THEORY

Kinetic theory is related to all phases, gaseous, liquid, and solid; however, it is most applied to gases. This is because the pressure of gases is highly related to the kinetics of different gas molecules at various temperatures. The assumption with gases is that atoms and molecules are in continuous random motion dependent on temperature.

Pressure of gases can be explained by kinetic theory. In a chamber of N numbers of gas molecules with a single molecule mass of m in a certain volume V will collide with one

another and with the walls of the container at a certain speed. Force can be described as occurring in the x and y and z directions. The force in one direction x will equal the change in pressure over the change in time or the Mass times the velocity in the x direction squared divided by the length L.

There are three assumptions when describing kinetic theory:

1. The gas has particles separated by large spaces and move in random directions.

2. The molecules undergo perfectly elastic conditions without loss of energy.

3. The transfer of kinetic energy between molecules is “heat”.

In such a case, force is exerted on a square area L-squared. Force is described in figure 72:

Figure 72.

Gas molecules will have specific molecular speeds, referred to as the MaxwellBoltzmann distribution. What this means is that there will be a variation in speeds, in which some speeds are fast and some are slow. There is a peak probability of speed of

particles that is related to the average molecular speed. Figure 73 describes the Maxwell-Boltzmann distribution of molecular speed at different temperatures.

Figure 73.

What this means is that the velocity of particles of gases will shift to higher speeds at higher temperatures and will be broadened by higher temperatures. As you can see, this is a probability distribution for ideal gases close to thermodynamic equilibrium. Heavier molecules will have a wider distribution (greater range of molecular speeds) but will be slower than lighter molecules. It applies to ideal gases.

Temperature is directly proportional to the average translational kinetic energy of molecules in an ideal gas. Heat applied to the system will indicate more rapid temperature of a gas molecule. This fact is crucial to the development of kinetic theory of gases. The gas in a container will exert an outward pressure on the walls of the container in elastic collisions with the sides of the container and with each other.

With these assumptions, you can determine that pressure times the volume equals the number of molecules multiplied by the temperature and by K, which is the Boltzmann constant. Using the equation as described in figure 72 and this equation, you get the equations described in figure 74:

Figure 74.

The average kinetic energy of a molecule is going to be one-half times the mass times the velocity squared. This relates then to the equation that the kinetic energy is equal to 1.5 times Boltzmann constant times the Temperature. This average kinetic energy of a molecule is referred to as the thermal energy. There are two components to the kinetic energy of a thermodynamic system, which are the kinetic energy plus the potential kinetic energy.

The kinetic energy is due to the motion of particles, such as rotation, vibration, and translational movements. In ideal gases, there is no inter-particle interaction. This means that there is no potential energy and only kinetic energy exists. With single-atom gases, such as the noble gases, there is just one atom in the gas. This is referred to as a monatomic gas. The kinetic energy is just the translational energy as there is no real rotational energy and no vibrational energy. This involves just three degrees of freedom—x axis, y axis, and z axis translation only.

Diatomic gases have five degrees of freedom: the three axes and two rotational degrees of freedom. With this, the internal energy U is equal to five-halves times N (the number of molecules) times Boltzmann constant times the temperature. With monatomic gases,