Question Detail
Question
An automobile tire is filled to a gauge pressure of 225 kPa at 25°C. After driving, the temperature rises to 48°C. What is the pressure within the tire now? (Assume constant volume).
Correct Answer
Option C is the correct answer.
Detailed Explanation
Using Gay-Lussac's law (P1/T1 = P2/T2) with absolute pressures and temperatures. P1_abs = 225 kPa + 101.3 kPa ≈ 326.3 kPa. T1 = 25 + 273 = 298 K. T2 = 48 + 273 = 321 K. P2_abs = P1_abs * (T2/T1) ≈ 326.3 * (321/298) ≈ 351.5 kPa. Gauge pressure = 351.5 - 101.3 ≈ 250.2 kPa.
Hint
Use the pressure-temperature relationship for an ideal gas at constant volume. Remember to use absolute pressure and temperature.