A bicycle tire is inflated to a gauge pressure of 3.71 atm when the temperature is 16°C. While a man rides the bicycle, the temperature of the tire rises to 45°C. Assuming the volume of the tire does not change, find the gauge pressure in the tire at the higher temperature.

Question

Kareem Brennan

Physics

14 December, 06:45

A bicycle tire is inflated to a gauge pressure of 3.71 atm when the temperature is 16°C. While a man rides the bicycle, the temperature of the tire rises to 45°C. Assuming the volume of the tire does not change, find the gauge pressure in the tire at the higher temperature.

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Answers (1)

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Brooklynn Singleton · Answer 1

The pressure of the tire will be 4.19 atm

Explanation:

The ideal gas equation is:

p0 * V0 / T0 = p1 * V1 / T1

Since V0 = V1 because the volume of the tire doesn't change

p0 / T0 = p1 / T1

p1 = p0 * T1 / T0

We need absolute temperatures for this equation

16 C = 289 K

45 C = 318 K

Now we replace the values:

p1 = 3.71 * 318 / 289 = 4.19 atm