## Related questions with answers

In an article on tire maintenance, it is stated that tires lose air over time, and pressure losses as high as 90 kPa (13 psi) per year are measured. The article recommends checking tire pressure at least once a month to avoid low tire pressure that hurts fuel efficiency and causes uneven thread wear on tires. Taking the beginning tire pressure to be 220 kPa (gage) and the atmospheric pressure to be 100 kPa, determine the fraction of air that can be lost from a tire per year.

Solution

VerifiedFirst we calculate the initial absoulte pressure in the tire:

$\begin{align*} P_{\text{abs}}&=P_{\text{gage}}+P_{\text{atm}}\\ &=220\:\text{kPa}+100\:\text{kPa}\\ &=320\:\text{kPa} \end{align*}$

Since the pressure in the tire is proportional to the weight of the air and therefore its mass, we can assume that the pressure loss is proportional to the mass loss. The percent of pressure loss than is:

$\begin{align*} \dfrac{\dfrac{\Delta P}{\Delta t}}{P_{\text{abs}}}&=\dfrac{\dfrac{90\:\text{kPa}}{\text{yr}}}{320\:\text{kPa}}\cdot100\%\\ &=\boxed{\dfrac{28\%}{\text{yr}}} \end{align*}$

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