Pressure vs. Temperature vs. Velocity Data


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.
 


Vapor Pressure vs. Temperature for Carbon Dioxide as a Function of % of Rated Fill


Vapor Pressure vs. Temperature for Carbon Dioxide

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.
 


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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