Question

In an article on tire maintenance, it is stated that tires lose air over time, and pressure losses as high as \(90 \mathrm{kPa}(13 \mathrm{psi})\) 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 \(220 \mathrm{kPa}\) (gage) and the atmospheric pressure to be \(100 \mathrm{kPa}\), determine the fraction of air that can be lost from a tire per year.

Short answer

Answer: Approximately 28.13% of air can be lost from a tire per year.

Step-by-step solution

Identify given values

We are given the following values: - Pressure loss per year: \(90\ \mathrm{kPa}\) - Initial tire pressure: \(220\ \mathrm{kPa} (gage)\) - Atmospheric pressure: \(100\ \mathrm{kPa}\)

Convert gage pressure to absolute pressure

To work with pressure values, we need to convert the gage pressure to absolute pressure. Absolute pressure is found by adding the gage pressure to the atmospheric pressure. In this case: Absolute pressure \(= 220\ \mathrm{kPa} (gage) + 100\ \mathrm{kPa} (atmospheric)\) Absolute pressure \(= 320\ \mathrm{kPa}\)

Calculate the fraction of air lost per year

Now that we have the absolute pressure, we can find the fraction of air lost per year by dividing the pressure loss per year by the absolute pressure. Fraction of air lost per year \(= \frac{90\ \mathrm{kPa}}{320\ \mathrm{kPa}}\) Fraction of air lost per year \(= 0.28125\)

Convert the fraction to a percentage for clarity

To better understand the result, we can convert the fraction to a percentage. Percentage of air lost per year \(= 0.28125 * 100\) Percentage of air lost per year \(= 28.13\ \%\) So, approximately \(28.13\ \%\) of air can be lost from a tire per year. This is why it is recommended to check tire pressure at least once a month to avoid low tire pressure that can damage fuel efficiency and cause uneven tire wear.

Key concepts

Gage Pressure

When we talk about the pressure in tires and other inflated objects, we often refer to gage pressure. This is the pressure that is measured relative to the atmospheric pressure, essentially the extra pressure within the tire over and above the outside air pressure. For example, when a tire's gage pressure is listed as 220 kPa, it means this is the pressure exerted by the air inside the tire above the standard atmospheric pressure of approximately 100 kPa.

Understanding gage pressure is crucial in automotive maintenance. It is this reading that most tire pressure gauges display and the one that drivers need to pay attention to when filling their tires. If the gage pressure is too low, tires can become inefficient and even unsafe. Monitoring and maintaining correct gage pressure helps ensure longevity of the tires and optimal fuel economy.

Absolute Pressure

Meanwhile, absolute pressure is a bit different from the gage pressure. It is the total pressure within the tire, including the atmospheric pressure. To get the absolute pressure of a tire, you add the atmospheric pressure to its gage pressure. In thermodynamic calculations, absolute pressure is important as it represents the true measure of the air molecules’ force within a tire without regard to the external environment.

For our previous example of 220 kPa gage pressure, the absolute pressure is calculated as 220 kPa plus the atmospheric pressure of 100 kPa, giving us 320 kPa in total. This number is essential for understanding the tire's true internal state and is used in calculations when considering any changes in volume or temperature, based on principles from the field of thermodynamics.

Pressure Loss

Pressure loss in tires can happen for several reasons such as temperature change, minor punctures, or simply over time. A tire can lose up to 90 kPa (13 psi) annually, according to the exercise's provided information. This loss can lead to under-inflated tires which have several drawbacks. Under-inflated tires have increased rolling resistance which means more effort is needed for the car to move and keep pace, reducing fuel efficiency.

Furthermore, pressure loss affects the tire’s contact with the road which can result in uneven wear, poor handling, and potential safety issues. Therefore, understanding and regularly checking for pressure loss is a key aspect of tire maintenance. Calculating the fraction or percentage of air lost helps drivers realize the importance of regular pressure checks to maintain tire health and vehicle safety.

Fuel Efficiency

Tire pressure directly impacts fuel efficiency. When tires are not inflated properly, they can't maintain their ideal shape, leading to an increase in rolling resistance. Essentially, more energy (and thus, more fuel) is required to move and keep the vehicle rolling. Ensuring tires are properly inflated minimizes rolling resistance and maximizes fuel efficiency.

As per the findings from the exercise, a potential 28.13% loss in tire pressure annually may significantly impact fuel economy. This translates to more frequent visits to the gas station and higher expense on fuel. Regular tire pressure checks and maintenance can contribute to an overall reduction in fuel consumption and carbon footprint, making it a simple yet effective practice for drivers who are looking to be both economically and environmentally responsible.