Problem 39 - General Chemistry: Principles and Modern Applications

Question

In a user's manual accompanying an American-made automobile, a typical gauge pressure for optimal performance of automobile tires is \(32 \mathrm{lb} / \mathrm{in} .^{2} .\) What is this pressure in grams per square centimeter and kilograms per square meter?

Step-by-Step Solution

Answer

The pressure in grams per square cm is 3.22 g/cm^2 and in kilograms per square meter is 322. Tracy kg/m^2 respectively.

Step 1: Conversion from lb/in^2 to g/cm^2

To convert from lb/in^2 to g/cm^2, First convert lb to g. Multiply the given value 32 lb / in^2 by 453.59237 g/lb. Then, convert in^2 to cm^2. The square of an inch is 6.45 cm^2. Divide the earlier determined value by 6.45 to get the value in g/cm^2.

Step 2: Conversion from g/cm^2 to kg/m^2

We convert g/cm^2 to kg/m^2. First, convert grams to kilograms. Since 1 g is equal to 0.001 kg, Multiply the prior step's result by 0.001. Then convert cm^2 to m^2. Since 1 cm is equal to 0.01 m, we have to square this to convert cm^2 to m^2. So multiply the obtained value in kg/cm^2 by 10000 (since (0.01)^2 is 0.0001, hence the value should be multiplied by 1/0.0001 = 10000 to convert cm^2 to m^2).

Step 3: Final answer

The final answers then are the pressures in grams per square centimeter (g/cm^2) and kilograms per square meter (kg/m^2).

Key Concepts

Gauge Pressure

In many applications, especially in automotive industries, gauge pressure is a term often encountered. It is the pressure measured relative to the local atmospheric pressure. Unlike absolute pressure, which includes atmospheric pressure, gauge pressure is convenient for measurements related to flow and level of liquids in tanks.

When measuring tire pressure, which is common in automobiles, gauge pressure does not account for atmospheric pressure. For example, in the problem at hand, the tire pressure is given as 32 lb/in², which refers to the gauge pressure.

For scientific accuracy, however, sometimes it might be necessary to convert gauge pressure to absolute pressure by adding atmospheric pressure to the gauge pressure reading.

Unit Conversion

Unit conversion is a crucial skill, especially in scientific and engineering fields. It involves changing the unit of a measurement to another unit while maintaining the same quantity. This is done using conversion factors, which are ratios that express the same quantity in different units.

In our problem, we perform several unit conversions:

• First, converting pounds per square inch (lb/in²) to grams per square centimeter (g/cm²). This involves two steps: converting pounds to grams and converting square inches to square centimeters.
• Second, the conversion from g/cm² to kilograms per square meter (kg/m²). Here, we change grams to kilograms and square centimeters to square meters.

Mastering unit conversion is essential for tackling real-world problems, where different unit systems might be in use.

Tire Pressure

Tire pressure is an essential parameter for the safety and performance of a vehicle. Proper tire pressure ensures optimum grip, fuel efficiency, and tire lifespan. Most cars will have a recommended tire pressure, typically expressed in pounds per square inch (psi). In the metric system, this may need to be converted to units like kilograms per square meter (kg/m²).

Tires that are under-inflated can lead to increased tire wear and reduced fuel efficiency. Over-inflated tires might have reduced traction and give a harsher ride. Therefore, regular checks of tire pressure using the gauge pressure in psi is a practical routine for vehicle maintenance.

SI Units

SI Units, or the International System of Units, form the basis for worldwide standard measurements. This system is used globally for scientific, engineering, and commercial measurements.

The core SI unit for pressure is the pascal (Pa), which is equivalent to one newton per square meter (N/m²). In engineering contexts, especially for tire pressure, common units are psi (non-SI) or can be converted to kg/m² in the metric system.

Converting to SI units ensures consistent and precise scientific communication. It avoids the misinterpretation that can occur when different regions use different units of measurement. Thus, converting measurements like tire pressure ensures clarity both in technical documentation and practical application.