Armand explained to his friend Bertrand that, in general, if you have a gas container and the amount of gas is doubled, the new pressure will be double the old pressure. The term "general" is employed because this is not exactly accurate, but it is close enough for the purposes of answering his next query.
Armand now posited this question to Bertrand, "If you have a tire filled with the standard 32 psi and you double the amount of air molecules in the tire, what pressure will your tire gauge now read? Assume that the tire does NOT expand, and that the first paragraph containing my initial information is exactly true."
Bertrand immediately answered, "64 psi."
But, Armand replied back to him, "Your answer is incorrect!"
What is the correct answer and why?
The gas law equation PV=mRT requires both temperature and pressure to be in absolute units. When you fill a tire to "32 psi", that is a gage pressure (what a tire gage would say), which is pressure relative to the outside atmosphere.
On the surface of the earth, the absolute air pressure is generally taken as 14.7 psi., so the 32 psi tire actually has an absolute pressure inside of 32+14.7=46.7psi. If you then double the amount of air molecules, you double the mass of air. With no change in temperature or volume, the absolute pressure doubles to 93.4 psi. A tire gage would then read 93.4-14.7=78.7psi
Another smaller but non-zero factor is how the tire is filled with the new/extra air. An air compressor adds heat to the air it compresses, so if that warmed air is put immediately into the tire, the air in the tire will be slightly warmer than the surroundings and will read a slightly higher pressure than the theoretical 78.7psi. When the air in the tire cools off for a while to the temperature of the surroundings, the gage pressure will approach 78.7 psi
Finally, let's assume that the air in the tank that will supply the tire was compressed yesterday, so that any added heat from the compression process is long gone. Since the tank is at higher pressure than the tire (required for the air to flow), the compressed air flowing through the hose and nozzle is a pressure reducing process, which, because it occurs relatively quickly, is a cooling process for the flowing air. Therefore, the air in the tire will be slightly cooled, resulting in a slightly lower pressure than the theoretical 78.7 psi., until such time as the air in the tire has returned to thermal equilibrium with the outside.
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Posted by Kenny M
on 2022-09-05 08:34:19 |
Solution
