On a winter -3.° C morning, the pressure in a car tire reads 28. psi on a pressure gauge. After several hours of highway traveling, the pressure reads 35. psi. Assuming the volume remains constant and normal atmospheric pressure of 15. psi, what is the tire temperature?
A) 45° C
B) 25° C
C) 41° C
D) 55° C
E) 55° F

Question

Quizplus · Accepted Answer

The relationship between pressure and temperature for a given volume of gas is described by the ideal gas law, which can be simplified to P1/T1 = P2/T2 when the volume and the amount of gas remain constant. Here, temperatures must be in Kelvin. The initial temperature is -3°C, which is 270 K (since 0°C = 273 K, -3°C = 270 K). The initial pressure (P1) is 28 psi, and the final pressure (P2) is 35 psi. We solve for T2 (final temperature in Kelvin) and then convert back to °C.T2 = (P2 * T1) / P1 = (35 psi * 270 K) / 28 psi = 341.25 KConverting back to Celsius: 341.25 K - 273 = 68.25°C, which is not an option provided. However, the correct approach should consider the absolute pressures by adding atmospheric pressure (15 psi) to the gauge pressures before applying the formula, because the ideal gas law uses absolute pressures. Thus, the corrected initial and final pressures are 43 psi (28 + 15) and 50 psi (35 + 15), respectively.T2 = (50 psi * 270 K) / 43 psi ≈ 314.0 KConverting back to Celsius: 314.0 K - 273 ≈ 41°C.Therefore, the correct answer is 41°C, which corresponds to choice C.

On a Winter -3