Scientific Principles that Make a Fire Piston Work
As the Mythbusters ® put it so eloquently
Warning Science Content!
The relationship between gas volume (V), pressure (P), and temperature
(T) can be expressed by the ideal gas law:
=
constant
where P = pressure of gas, V = volume occupied, and T = temperature.
In simpler terms, if volume is constant, an increase in temperature results
in a proportional increase in pressure. If pressure is constant,
an increase in temperature results in a proportional increase in volume. Inversely,
if volume is decreased and pressure remains constant, temperature must
decrease. Basically, pressure and volume are directly proportional
to temperature and inversely proportional to each other.
The special situation of a fire piston differs slightly from Charles'
Law due to the fact that the change in pressure occurs so rapidly. In
this case a process know as adiabatic heating occurs.
"Adiabatic heating is a process that commonly occurs due to a change in the pressure of a gas. Adiabatic heating occurs when the pressure of a gas is increased. An example of this is what goes on in a bicycle pump. After using a pump to inflate a pneumatic tire or ball, the barrel of the pump is found to have heated up as a result of adiabatic heating. Diesel engines rely on adiabatic heating during their compression stroke to elevate the temperature sufficiently to ignite the fuel." (wikipedia)
To summarize this content if you take a volume of gas and decrease volume rapidly by increasing the pressure, the temperature of that gas gets hot really fast. The greater the increase in pressure and decrease in volume the hotter it gets. So a fire piston with a narrow diameter and long stroke can get very hot with just a small amount of effort.
If you are interested in some really complex mathematical equations check out (wikipedia).