Question

Footballs used by the NFL are inflated to 12.5 psi. 11 of 12 footballs measured 10.5 psi after the playoff game when the temperature was 5°C. At what temperature were the balls inflated to explain this pressure drop?

Answer 1

Answer: 331 K

Explanation:

To calculate the temperature of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where,

$P_1\text{ and }T_1$ are the initial pressure and temperature of the gas.

$P_2\text{ and }T_2$ are the final pressure and temperature of the gas.

We are given:

$P_1=12.5psi\\T_1=?\\P_2=10.5psi\\T_2=5^0C=(5+273)K=278K$

Putting values in above equation, we get:

$\frac{12.5}{T_1}=\frac{10.5}{278}\\\\T_1=331K$

Hence, the temperature at which the balls inflated to explain this pressure drop is 331 K