The ideal gas law, first stated in 1834, has suddenly become big news.
The law, which describes a relationship between temperature and pressure, hit the national news scene recently after players in the NFL's AFC championship game between the New England Patriots and Indianapolis Colts noticed that the balls were, well, soft. Measurements ensued, fingers were pointed, and within days the nation was treated to the sight of Patriots coach Bill Belichick attempting to explain the relationship between temperature and pressure in a gaseous system. “The preparation of the ball caused the ball to be, I would say, artificially high in psi,” he said during a press conference that was called to address the unexpected effects of the ideal gas law. “It reached its equilibrium at some point later on -- you know, an hour, two hours. That level (in psi) was below what was set in this climatic condition.” (The game was played in New England.)
In a broad scientific sense, Belichick’s fumbling explanation was, in fact, correct. According to the ideal gas law, a rise in temperature (assuming all other factors are equal) causes a rise in pressure. “The more the temperature goes up, the more the molecules fly around,” Eric Nauman, professor of mechanical engineering at Purdue University, told Design News. “The faster they go, the harder they bang into each other, and the harder they bang into the walls of an air cylinder or a football. And when they push against the walls, the pressure goes up.”
Motion control engineers know this phenomenon all too well. Ultra-precise positioning systems powered by air can be affected by temperature. The caveat, however, is that it must be a large temperature swing, they say. “If you set up a system with a positioning accuracy of hundredths of an inch in a 70 degree room, and then you deploy it in a -10 degree room, yes, you will definitely get different measurements,” said Frank Langro, director of marketing and product management for Festo Corp., a manufacturer of pneumatic systems. Langro adds that NASA engineers face those temperature-related challenges all the time when deploying air-powered systems inside spacecraft.
But as Langro points out, the temperature swings must be vast. As would be expected, a small temperature swing causes a small change in pressure. That’s why the claim that the balls lost between 1.5 psi and 2.0 psi as the result of a 20F temperature swing seems unlikely. “By my estimates, the ball should have gone from 12.5 psi to 12.1 psi, based on a 20 degree temperature change,” Nauman told us.
Then there’s the issue of time. Experts say that car tires lose three or four psi over the course of months -- from July to January, for example. The same holds true for basketballs and volleyballs -- they go flat after weeks, not hours, in a car trunk. ”Some processes are fast and some are slow,” Langro told us. “Temperature is a slow process.”
The bottom line is that Belichick’s reliance on the ideal gas law, while broadly correct, falls flat on the details. “It’s too much pressure drop, too little time,” Langro said. “That’s where Bill Belichick needs to go back to school.”
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