Final answer:
To find the required final temperature for the pressure in an automobile tire to increase from 2.15 atm to 2.37 atm at constant volume and amount, use Gay-Lussac's law to solve for the unknown temperature after converting all temperatures to Kelvin.
Step-by-step explanation:
The subject of this question is ideal gas behavior, specifically understanding how changes in temperature affect gas pressure when volume and amount of gas are held constant, according to Gay-Lussac's law. This law can be stated mathematically as P1/T1 = P2/T2, where P represents pressure and T represents temperature measured in Kelvins. To solve this question, first, convert the temperatures from Celsius to Kelvin (T(K) = T(°C) + 273.15). Then apply the formula with the given values (P1 = 2.15 atm and T1 = 0°C or 273.15 K; P2 = 2.37 atm and T2 = unknown).
Start by rearranging the formula to solve for T2: T2 = (P2 × T1) / P1. Plug in the values T2 = (2.37 atm × 273.15 K) / 2.15 atm. After the calculation, convert the Kelvin temperature back to Celsius to find the final temperature required for the pressure inside an automobile tire to increase as described in the question.