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Deflate-Gate and PV/T=k

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This Deflate-Gate controversy had me thinking about 9th grade chemistry and wondering about the effect of temperature on the balls. I saw that CAR kicker Graham Gano recently tweeted that he is often frustrated by how the balls naturally lose their air pressure when going from an indoor setting, where the inflation pressure is set and checked, to a cold outdoor setting. Could NE's balls have lost their pressure due to the temperature?

We'll need to dust off the Combined Gas Law to figure this one out. That's the physical law that says gas temperature, pressure, and volume are all related. Pressure and temperature are directly proportional--As temperature goes up, pressure goes up proportionally and vice versa. Pressure and volume are inversely proportional--as volume expands, pressure decreases and vice versa. And so it follows that volume and temperature must also be directly proportional. Put mathematically, we can say that for a given mass of air, the ratio of product of the pressure and volume and the temperature must remain constant.

PV/T = k (where k is a fixed constant)

If we change any one of those variables, we can solve for the others. Because k=k, we can write:

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