Question

The U.S. gets \(2.4\) qBtu per year of energy from burning biomass (mostly firewood). At an energy density of 4 kcal per gram, and a population of 330 million, how many 5 kg logs per year does this translate to per person?

Short answer

Answer: The United States consumes approximately 91.64 5 kg logs per person per year from burning biomass.

Step-by-step solution

Convert energy from qBtu to kcal

We need to convert the given 2.4 qBtu to kcal. 1 Btu is equivalent to 0.252 kcal. Therefore, we have: \(2.4\,\text{qBtu} \times 10^15\,\text{Btu/qBtu} \times 0.252\, \text{kcal/Btu} = 6.048 \times 10^{14}\, \text{kcal}\)

Calculate the total mass of biomass consumed in grams

Now, we will calculate the total mass of biomass burned with energy density 4 kcal per gram. We do this by dividing the kcal by the energy density as follows: \(\frac{6.048 \times 10^{14}\, \text{kcal}}{4\, \text{kcal/g}} = 1.512 \times 10^{14}\, \text{g}\)

Convert grams to kilograms

Now, let's convert grams into kilograms to make it easier to relate with the given log mass (5 kg): \(1.512 \times 10^{14}\, \text{g} \times \frac{1\, \text{kg}}{1000\, \text{g}} = 1.512 \times 10^{11}\, \text{kg}\)

Calculate number of 5 kg logs

Next, we'll calculate the total number of 5 kg logs this mass represents: \(\frac{1.512 \times 10^{11}\, \text{kg}}{5\, \text{kg/log}} = 3.024 \times 10^{10}\, \text{logs}\)

Calculate number of 5 kg logs per person

Finally, we will divide the number of logs by the population of the United States to calculate the number of logs per person: \(\frac{3.024 \times 10^{10}\, \text{logs}}{330 \times 10^6\, \text{people}} \approx 91.64\, \text{logs/person}\) Thus, the consumption of burning biomass (mostly firewood) in the United States translates to approximately 91.64 5 kg logs per person per year.

Key concepts

Energy Density Calculation

Understanding how to calculate energy density is key to managing energy resources and evaluating their sustainability. Energy density refers to the amount of energy stored in a given system or region of space per unit volume or mass. In our exercise, energy density is specified for biomass as 4 kilocalories per gram (kcal/g). The task was to connect energy consumption in quadrillion British thermal units (qBtu) with the amount of biomass, measured in kilograms, that provides this energy.

By defining energy density in such a clear manner, it makes the conversion between the energy content and the physical quantity of biomass straightforward. For instance, knowing that 1 gram of biomass releases 4 kcal when burned, we can calculate the mass of biomass needed to meet a specific energy requirement. This dimension of energy density is particularly important when comparing the efficiency and utility of different fuels or energy sources, whether they are solid like wood or liquid like petroleum.

Unit Conversion

Unit conversion is an indispensable skill in science, engineering, and daily life, ensuring that measurements are communicated and understood universally. In the exercise, we were presented with energy measured in qBtu, a unit unfamiliar to many, and converted it to the more commonly used kcal. The conversion factor used is that 1 Btu is equivalent to 0.252 kcal.

Being adept at unit conversion involves understanding the relationships between units and applying the appropriate conversion factors. Mathematically, the conversion is achieved through multiplication by a ratio that represents the number of one type of unit per another. This ratio is essentially '1' expressed in different units, as it equates different quantities of the same dimension. This method avoids any change in the actual size or value of the measurement but simply expresses it in a different scale.

Biomass Consumption Per Capita

Biomass consumption per capita is a measurement that can give insights into a country's renewable energy usage and its environmental impact. It denotes the amount of biomass energy used on average by each person in a given population. In our exercise, we translated the total energy obtained from biomass in the United States into the number of 5 kg logs used per person per year.

The calculation for per capita consumption allows us to contextualize large-scale statistics on a level that relates to the individual. By dividing the total number of logs by the United States population, we get a graspable figure that exhibits an individual's share in the nation's energy consumption. This statistic becomes especially interesting when comparing different countries or regions, showcasing how reliant or efficient they are in using biomass as an energy source.