Final answer:
After calculating T1, we will have our answer in Kelvin, which can be converted back to degrees Celsius by subtracting 273.15.
Step-by-step explanation:
To determine at what temperature the NFL footballs were inflated before the pressure dropped to 10.5 psi from 12.5 psi, we can use the ideal gas law and assume that the volume of the footballs remains constant (since they're made of materials that don't expand or contract much with temperature). The ideal gas law implies a direct relationship between pressure and temperature, meaning that if the temperature drops, the pressure will also drop, provided the number of moles of gas and the volume remain constant.
Starting with the initial condition, where P1 = 12.5 psi and the final condition where P2 = 10.5 psi at T2 = 5°C, we can find the initial temperature (T1) using the following relation from Charles's Law:
P1/T1 = P2/T2
However, to use this formula, we need to convert the temperatures into Kelvin:
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- T2 (in Kelvin) = 5°C + 273.15 = 278.15 K
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- T1 = (P1 * T2) / P2
T1 = (12.5 psi × 278.15 K) / 10.5 psi
After calculating T1, we will have our answer in Kelvin, which can be converted back to degrees Celsius by subtracting 273.15.