air pressure of an automobile

Question

 The air pressure in the tires of an automobile is adjusted to 2.3 atm at a gas station in San Diego, where the air temperature is 20°C (68°F) and atmospheric pressure is 0.987 atm. After a 3-hour drive along Interstate 8 (I-8), the car and driver are in Yuma, Arizona, where the temperature is 43°C (110°F). What is the pressure in the tires, if we assume that atmospheric pressure is still 0.987 atm? Note: The measured tire pressures are gauge pressures, meaning that they indicate the pressures in the tires above atmospheric pressure.

Answer 1

About 2.6 atm on the gauge (3.54 atm absolute).

That note about gauge pressure is not a footnote — it is the entire problem. Gas laws require absolute pressure, and the tire gauge does not report it.

Step 1 — convert gauge to absolute

P_abs = P_gauge + P_atm = 2.3 + 0.987 = 3.287 atm

A gauge reads zero in open air, so it is measuring how much the tire exceeds its surroundings. The gas inside does not know about that offset — it responds to the total pressure it actually exerts.

Step 2 — convert temperatures to kelvin

T₁ = 20 + 273.15 = 293.15 K
T₂ = 43 + 273.15 = 316.15 K

Celsius will not work here either. The ratio 43/20 = 2.15 would predict the pressure more than doubling; the true ratio is 316.15/293.15 = 1.078, a 7.8% rise. Kelvin is required because gas laws are proportionalities, and only an absolute scale makes ratios meaningful.

Step 3 — Gay-Lussac's law (volume and moles fixed, since a tire is rigid and sealed)

P₁/T₁ = P₂/T₂

P₂ = (3.287 atm)(316.15 / 293.15) = 3.545 atm absolute

Step 4 — back to gauge, since that is what the question asks

P_gauge = 3.545 − 0.987 = 2.56 ≈ 2.6 atm

Why the conversion matters numerically

Skip it and apply the temperature ratio straight to the gauge reading: 2.3 × 1.078 = 2.48 atm. That is off by about 0.08 atm — a small-looking gap that is entirely an artifact of using the wrong pressure scale. Convert → solve → convert back, every time.

The practical version of this result: a 23 °C temperature rise added roughly 0.26 atm (about 3.8 psi) to the tires. This is why you check tire pressure when the tires are cold, and why pressure warnings often appear on the first cold morning of autumn — nothing leaked, the air just cooled.