Final answer:
The final temperature of the bicycle tires, when the pressure changed from 2.1 atm to 1.9 atm and the initial temperature was 43°C, is approximately 12.8°C.
Step-by-step explanation:
To determine what the final temperature was when your bicycle tires changed from 2.1 atm to 1.9 atm, we can use the relationship between pressure and temperature of a gas, which is described by Gay-Lussac's Law. This law states that the pressure of a gas is directly proportional to its temperature when the volume and the amount of gas are held constant.
We can set up the proportion as follows:
P1 / T1 = P2 / T2
Where:
- P1 is the initial pressure (2.1 atm)
- T1 is the initial temperature in Kelvin (43°C + 273.15 = 316.15 K)
- P2 is the final pressure (1.9 atm)
- T2 is the final temperature in Kelvin (what we are solving for)
By rearranging the equation to solve for T2, we get:
T2 = (P2 × T1) / P1
T2 = (1.9 atm × 316.15 K) / 2.1 atm
Now, calculate T2:
T2 = 285.971 K
Finally, to find the temperature in Celsius, we subtract 273.15 from the Kelvin temperature:
Final Temperature = 285.971 K - 273.15 = 12.821°C
The final temperature of the bicycle tires is approximately 12.8°C.