Gas Law and Kinetic Theory

by Michael Pryor

This is a representation of the conservation of energy. This is a very poor example, because the light bulb cannot charge the battery. A better example would be to view the Q as something that either produces or gives off heat specifically and then something that either takes work or does work itself. Although the light bulb does give off heat, it is not a good example of its change in energy. An oven is a good example of a change in temperature, but a poor example of doing work, because the work does is not visually apparent. 

In the perspective of the gas laws, work is equal to pressure of a change in volume.
Given that pressure is constant, then the change in volume can be displayed as the change in volume due to the coefficient of heat expansion. The initial volume is the mass divided by the density.
The mass is calculated using the specific heat and the change in temperature.
This shows that because of the density of this object the heat that the object absorbs is much greater than the work that the object does in its expansion due to its change in energy.

Force is equal to the change in pressure over an area. This means pressure is also equal to a force over an area.
If the mass is constant then force is equal to the mass multiplied by the change in velocity, or the velocity squared divided by its displacement.
 Given that the area is a square, its formula is is x squared.
The new formula becomes the sum of the mass multiplied by velocity in one direction squared all divided by the displacement (x) cubed.
The numerator is very similar to the formula for kinetic energy. If that adjustment is made to include the kinetic energy of a an atom in a gaseous state, then the numerator must be multiplied by two and the number of atoms must be accounted for, The atom moves in three dimensions, this means that there is an adjustment of 3. This is proved when you calculate the magnitude of the cube and you make all three dimensions equal, as in a cube.

 Given the initial equation that PV=2/3N*E=N*Kb*T where Kb is the Boltzman constant.
Kinetic energy can be equated to 3/2*Kb*T and that can be equated to 1/2*m*(v)squared
Velocity is then equal to the square root of (3*Kb*T)/m
If Q is equal to W then there is no change in the energy of the system.
Which means the equation is in equilibrium and any fluctuation are met with equal values on either side of the equation.
Given a constant pressure and a constant number of molecules. The question can be redced to 3/2*The change in temperature/actual temperature=the opposite of the change in volume/actual volume
When both sides are integrated, the temperature to the -3/2 power is equal to the volume.

These calculations better represent the calculation of force from a change in pressure over a change in temperature, From the earlier equation in which force equals the change in mass multiplied by velocity plus the change in velocity multiplied by mass.

In this experiment the change in volume equates to a change in temperature. As the volume decreases then temperature must increase, because there is no significant change being done to the energy in the system.
Theoretically the final temperature inside the syringe is 604 K this is a significant jump from its original temperature of
293 K and is enough to light a small piece of cotton on fire inside of the syringe.

Physics like a Boss.