The sticker inside the door of my car says that the tire pressure should be 32 psig (322 kPa) when the tire is cold. Before a road trip, I fill the tire to this pressure on a cold morning when the temperature is 15 °C, and then head out towards Las Vegas. When I make a rest stop in Barstow, it is now quite warm out, and the air in my tires has also warmed up from friction during the long drive. So, the air in the tires is now 60 °C. Assuming my tires don't leak or expand (volume is constant), what is the expected tire pressure at this rest stop?

Question

Engineering

Jagger Ford

20 August, 06:17

The sticker inside the door of my car says that the tire pressure should be 32 psig (322 kPa) when the tire is cold. Before a road trip, I fill the tire to this pressure on a cold morning when the temperature is 15 °C, and then head out towards Las Vegas. When I make a rest stop in Barstow, it is now quite warm out, and the air in my tires has also warmed up from friction during the long drive. So, the air in the tires is now 60 °C. Assuming my tires don't leak or expand (volume is constant), what is the expected tire pressure at this rest stop?

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Answers (1)

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Hood · Answer 1

37 psi

Explanation:

For ideal gases this equation applies:

p1*V1/T1 = p2*V2/T2

Since we are assuming volume remains constant:

V2 = V1

p1/T1 = p2/T2

p2 = p1*T2/T1

The temperatures must be in absolute scale.

T1 = 15 + 273 = 288 K

T2 = 60 + 273 = 333 K

Then:

p2 = 32 * 333 / 288 = 37 psi