Question

The pressure in an automobile tire is 198 kPa at 27 °C. At the end of a trip on a hot sunny day, the pressure has risen to 225 kPa. What is the temperature of the air in the tire?

a) 81.44°C
b) 93.33°C
c) 99.12°C
d) 107.05°C

Answer 1

Using Gay-Lussac's law and the ideal gas law, the temperature of the air in the tire when the pressure has risen from 198 kPa to 225 kPa, assuming no change in volume, can be calculated to be approximately 68.14 °C. This doesn't match any of the provided options.

Step-by-step explanation:

To figure out the temperature of the air in the tire after the pressure rise, we will use the ideal gas law which assumes no change in volume or amount of gas. The relationship between pressure and temperature for a given volume and quantity of gas is given by Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature when volume and amount are held constant. Therefore, we calculate the new temperature (in Kelvins) with the formula T2 = (P2/P1) * T1, where T1 is the initial temperature, P1 is the initial pressure, and P2 is the final pressure.

First, convert the temperatures from Celsius to Kelvin. T1 in Kelvin is 27 °C + 273.15 = 300.15 K. Then plug in known values into the equation: T2 = (225 kPa / 198 kPa) * 300.15 K.

Doing the math gives us T2 ≈ 341.29 K, which we can convert back to Celsius by subtracting 273.15, yielding a final temperature of about 68.14 °C. Therefore, none of the provided options (a-d) is correct.