Kinetic Theory and PV Diagrams

The air in a glass syringe will expand as it is dipped in hot water, causing the syringe to rise. It will condense once it's temperature drops, pulling in the syringe.

Another group also compared internal energy to a measure of how hyper a kid is. The more candy the kid has, the more internal energy he has. However, if the kid plays or monkeys around all day, his internal energy will go down.

Isochoric Processes undergo no volume change, there for there is no work done, similar to a cooling cup of coffee. The change in internal energy equals the amount of energy added. In an adiabatic process, there is no energy added, and the change in internal energy equals the work done by the system, much like the compression and expansion of a cylinder in a car engine.

From Newton's second law that force equals the change in momentum per unit of time, and since the velocity vectors only change direction, a system of gas particles exerts a force equal to (2mv)/(t,final - t,initial).v

The work done by a system as it is heated equals the volume change multiplied by its pressure. We use the volume thermal expansion formula, and the relation between volume and density to substitute for the original volume of the system.

The pressure of an ideal gas system is actually equal to 2/3 of the total energy of the system multiplied by the number of molecules per unit volume. 

Since the internal energy of a system is dependent only on temperature, an isothermal reaction has zero change in internal energy, and work equal energy. For a an adiabatic process, energy neither enters nor exits the system, and the change in internal energy equals the work done by the system.

Here is a fire syringe used to perform an adiabatic process by rapidly condensing the volume of the cylinder, which in turn raises the temperature of the cylinder effectively causing the piece of cotton inside to ignite.

The greek letter gamma represents the ratio of heat capacities of air. A final temperature of 690 K is predicted, which is well above papers flashpoint of 506 K. This means the work performed on the gas by the collapsing piston was enough to raise the temperature of the chamber above the minimum required to burn the cotton.