Final answer:
To find the new gauge pressure of a tire when the temperature increases, use the Ideal Gas Law formula P1/T1 = P2/T2, convert temperatures to Kelvin, and rearrange to solve for P2.
Step-by-step explanation:
The question refers to calculating the new gauge pressure of a tire when its temperature increases from 15°C to 38°C while maintaining the same volume. According to the Ideal Gas Law, pressure directly varies with temperature when volume and the amount of gas are constant.
Using the formula P1/T1 = P2/T2 (where P is pressure, T is temperature in Kelvin, and the subscripts 1 and 2 refer to the initial and final states, respectively), we can find the new pressure.
First, convert temperatures to Kelvin by adding 273.15:
15°C = 288.15 K
38°C = 311.15 K
Then, rearrange the formula to solve for P2: P2 = P1 × (T2/T1)
Substitute the given values into the equation: P2 = (2.2 × 10⁵ Pa) × (311.15 K / 288.15 K)
After calculating the right-hand side, the result will give the final gauge pressure in the tire after the temperature change.