A student rides a bicycle to class every day, a 10.-mile round trip that takes 30 . minutes in each direction. The student burns \(1250 \mathrm{~kJ} \cdot \mathrm{h}^{-1}\) cycling. The same round trip in an automobile would require \(0.40\) gallons of gasoline. Assume that the student goes to class 150 days per year and that the enthalpy of combustion of gasoline can be approximated by that of octane, which has a density of \(0.702 \mathrm{~g}^{\cdot \mathrm{cm}^{-3}}(3.785 \mathrm{~L}=1.000 \mathrm{gal})\). What is the yearly energy requirement of this journey by (a) bicycle and (b) automobile?

When discussing energy requirements in transportation, it's crucial to understand the concept of enthalpy of combustion. This term refers to the amount of energy released when a substance combusts in the presence of oxygen. It's typically measured in kilojoules per mole (kJ/mol) and is usually negative because combustion releases energy. For example, octane, which we use to approximate the enthalpy of combustion for gasoline, releases energy when burned. This release of energy powers vehicles, allowing them to move.

The enthalpy of combustion is an important value when comparing different fuels, as it provides a measure of the energy output that can be expected from a given amount of fuel. Higher values mean more energy per mole of fuel, and thus, more power available for transportation. In the example given, the enthalpy of combustion of octane is -5471 kJ/mol, which indicates that each mole of octane releases 5471 kJ of energy when burned completely.

Calculating energy expenditure is essential when comparing different modes of transportation. Energy expenditure can refer to the amount of energy a person uses to perform an activity, such as cycling, or the amount of energy a vehicle consumes to operate.

In our exercise, two calculations are required: one for the bicycle and one for the automobile. For cycling, the calculation starts with the rate of energy expenditure given as 1250 kJ/hr. By converting this hourly rate to a daily rate and then to an annual rate, factoring in the number of days the activity is performed, we can determine the yearly energy requirement for the bicycle. Such calculations help individuals understand the energy cost of different activities and can influence decisions in personal transportation methods.

Understanding various energy units and how to convert between them is vital in energy-related problems. Common energy units include joules (J), kilojoules (kJ), calories (cal), watts (W), and British Thermal Units (BTU). In practical applications like transportation, fuels are often measured in gallons or liters, which are then converted to energy units through their relationship to density and energy content.

In our example, gallons of gasoline need to be converted to the energy they can produce. This process involves several unit conversions, such as turning gallons to liters, liters to mass using the density of the fuel, mass to moles using the molar mass, and finally, moles to energy using the enthalpy of combustion. Such conversions are commonplace in exercises that deal with energy requirements and are a fundamental skill for students to learn.

The density of a fuel, combined with its energy content, gives us a complete picture of the fuel's energy potential. The density, typically measured in grams per cubic centimeter (g/cm³) for liquids, is used to convert volume to mass, as seen with octane in the given exercise.

By knowing the density, we can determine the mass of fuel consumed, and consequently, its energy content. The energy content is directly related to the enthalpy of combustion and indicates how much energy can be obtained from a certain mass of fuel. In transportation, the density and energy content of fuels are critical for calculating fuel efficiency and the environmental impact of different transportation methods. Using the automobile in the exercise as an example, understanding the relationship between the density of gasoline and its energy content helps calculate the total energy usage over the course of a year.