Solving for Gauge Pressure Changes in a Tire During Descent

How does the gauge pressure in a tire change as a car descends from a mountain to sea level?

Given the initial conditions of the tire at the mountain top and the final conditions at sea level, what will be the gauge pressure inside the tire?

Answer:

The gauge pressure of the tire at sea level will be higher.

When a car descends from a mountain top to sea level, the atmospheric pressure changes. This change in pressure affects the gauge pressure inside the tire. The gauge pressure is calculated based on the absolute pressure inside the tire and the atmospheric pressure at the specific location.

Initially, the tire has a gauge pressure of 30 psi at the mountain top where the atmospheric pressure is 0.7 atm. Using the relation between gauge pressure, absolute pressure, and atmospheric pressure, we calculate the absolute pressure inside the tire to be 2.74 atm at the mountain top.

As the car descends to sea level, the atmospheric pressure increases to 1.0 atm. The temperature inside the tire also increases to 350 K. Using the ideal gas law and the assumption of no leaks, we can determine that the gauge pressure inside the tire at sea level will be higher than it was at the mountain top.

After performing the calculations, we find that the gauge pressure of the tire at sea level will be 37.42 psi. This increase in gauge pressure is a result of the changes in temperature and atmospheric pressure during the descent. Therefore, the gauge pressure inside the tire increases as the car moves from the mountain top to sea level.