A tire is filled with air at 20^oC to a gauge pressure of 200 kPa. Then the tire reaches a temperature of 40^oC. The fraction of the original air that must be removed if the original pressure of 200 kPa is to be maintained is

Question

Quizplus · Accepted Answer

To maintain the original pressure of 200 kPa after the temperature increase, we use the ideal gas law, which implies that pressure is directly proportional to temperature when volume and the amount of gas are constant. The temperature increases from 20°C to 40°C, which in Kelvin is from 293K to 313K. The fraction of air to be removed to maintain the original pressure can be calculated using the formula derived from the ideal gas law: (T2 - T1) / T2 = (313K - 293K) / 313K = 20/313 ≈ 0.064 or 6.4%.

A Tire Is Filled with Air at 20oC to a Gauge

A Tire Is Filled with Air at 20^oC to a Gauge