The Patriots inflated each game ball to 13.0 psi prior while indoors at 85.0 F. Then, the footballs were placed and let sit in 38.0 F weather. After cooling, what is the pressure inside the football?

Question

The New England Patriots in the National Football League (NFL) were accused of under-inflating footballs to give them a competitive advantage. The NFL requires footballs to be inflating to a minimum pressure of 12.5 psi (pounds per square inch).

Answer 1

If we assume that the football is stiff enough that its volume does not change with inflation (over the range of inflation this problem is considering) and we also assume no air escapes, then we can use Gay-Lussac's Law:

Where P₁ = 13.0 psi and T₁ is (converting to Kelvin) (5)(85 - 32)/9 + 273.15 = 302.59 K

And where T₂ is (converting to Kelvin) (5)(38 - 32)/9 + 273.15 = 276.48 K

Then:

13.0/302.59 = P₂/276.48 and cross multiplying:

13(276.48) = (302.59)(P₂)

P₂ = 11.9 psi