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Pressure vs. Temperature vs. Velocity Data |
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A CO2
cylinder, when new, contains a mixture of liquid and gaseous
carbon dioxide. The pressure of the gaseous CO2
above the liquid CO2 is called the
vapor pressure of CO2 and is a
property of the liquid and a function of temperature. At any
given temperature, the vapor pressure of CO2 remains constant as long
as there is some liquid CO2 still in the cylinder. The vapor
pressure vs. temperature relationship for CO2
is illustrated in the figures below.
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Vapor Pressure vs. Temperature for
Carbon Dioxide as a Function of % of Rated Fill |
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Vapor Pressure vs. Temperature for Carbon Dioxide |
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When a CO2-powered
pistol is fired, the release of gas from the cylinder
causes the temperature of the cylinder's contents to drop due to
the loss of molecules that have the greatest kinetic energy.
This lowers the average kinetic energy of the remaining
molecules, which we observe as a decrease in temperature. The drop
in temperature results in a decrease in vapor pressure. In
addition, the rapidly expanding CO2
escaping through the hole in the cylinder undergoes
Joule-Thomson cooling, which cools the area surrounding the neck
of the cylinder, including the gun's valve and the CO2
cylinder itself. If
several shots are fired within a short period of time, each
successive shot will have a lower velocity since the pressure of
CO2 available to propel the pellet is
decreasing due to cooling of the cylinder's contents. If the shots are spread over a longer period of
time, the CO2 cylinder will have a chance
to absorb energy from its surroundings and warm up, which will
increase the vapor pressure. If the CO2
cylinder is allowed to warm up to its original temperature, then
the vapor pressure of CO2 in the cylinder
will return to its original pressure. When all of the liquid CO2
is gone from the cylinder and only gaseous CO2
remains, the pressure of CO2 in the
cylinder is approximated by the Ideal Gas Law (P=nRT/V). At this
point, the gas pressure in the cylinder decreases with every
shot since n (moles of gas) is decreasing with each shot.
The figures below illustrate the relationships between
temperature, pellet velocity, and shot frequency. All tests were
conducted using a Daisy 617X air pistol loaded with Crosman
CO2 cylinders and firing Gamo
Match pellets. Temperature vs. time measurements were made using
a thermistor encased in a stainless steel tube and connected to
a MicroLab data acquisition unit.
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Testing Setup |

Closeup of Thermistor Placement |

This test involved firing a shot, waiting for
the temperature to return to its initial value, then firing a
second shot. This test demonstrates that a CO2
cylinder will return to its initial temperature within
approximately three minutes after a shot is fired with a
corresponding restoration of shot velocity. Notice that the
cylinder reaches its maximum drop in temperature approximately
one minute after the shot. The maximum drop in temperature was
0.24 șC. |

In this test, shots were fired at one minute
intervals for three minutes. The decrease in velocity is not as
pronounced since there is some warming of the cylinder that
occurs between shots. Notice that within one minute of a shot
being fired, the cylinder is starting to warm up again. The
overall decrease in temperature was 0.32 șC. |

In this test, shots were fired every 15
seconds for 75 seconds. With a shot interval this short, there
is no warming of the cylinder between shots. The maximum drop in
temperature over the time shots were fired was 0.45 șC. |

This chart illustrates the effects of firing
five shots 1 second apart (rapid fire). Not only is there a
large decrease in projectile velocity (about 30 fps), but the
temperature of the cylinder (and its surroundings) will take
much longer than three minutes to return to the initial value.
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