5. In the January 2015 AFC championship football game in 500°F weather, the New

Question

5. In the January 2015 AFC championship football game in 500°F weather, the New England Patriots won against the Indianapolis Colts. However, after the game, it came to light that many of the footballs used by the Patriots on offense were underinflated by 2 psi (NFL regulations require that footballs be inflated to between 27.2-28.2 psi)?. Could there be a innocent explanation for this, or were the Patriots cheating? Assume the balls were inflate 25.2 psi when the under-inflation was discovered. °C-Tag, K-T+ 2 d to 1.8 Assuming the footballs didn't have leaks, what factors are being held constant in this scenario? What relationship will we use for this calculation? a. At what minimum temperature must the balls have originally been inflated if they had deflated by 2 psi under game conditions? Report your answer in units of degrees Fahrenheit. b.

Explanation / Answer

(a)

Since there are no leaks, this means that the number of moles of the air inside the ball does not change. Also since the pressure drop is not very much, so the volume also remains constant.

In this case we will use the ideal gas equation:

PV = nRT

'n', R and V will be constant here. So P is directly proportional to T.

Thus as the outside temperature drops, the ball gets deflated because it's internal pressure also gets reduced.

Hence the team is not cheating but the deflation occured due to a natural phenomenon.

(b)

500F = 283.15 K

Using relation:

P1/T1 = P2/T2

Putting values:

25.2/283.15 = 27.2/T2

Solving we get:

T2 = 305.62 K = 90.450F

Hope this helps !

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