Question

A typical college campus is probably about one square kilometer in area. How much power out of Earth's 44 TW geothermal budget passes through the campus area, assuming uniform distribution across the \(5.1 \times 10^{8}\) square kilometers of earth's surface? How does this compare to a typical college electrical demand of about \(20 \mathrm{MW} ?\)

Short answer

The geothermal power passing through a typical college campus is about 4.315 x 10^(-4)% of the college's electrical demand. This demonstrates that the geothermal power is significantly lower than the typical college's electrical demand.

Step-by-step solution

Calculate the geothermal power density of the Earth

The geothermal power density can be found by dividing the Earth's geothermal power (44 TW) by its surface area. The given surface area is \(5.1 \times 10^{8}\) square kilometers. Geothermal power density = (Total geothermal power) / (Earth's surface area) Power Density = \(\frac{44 \times 10^6 \,\text{kW}}{5.1 \times 10^{8}\,\text{km}^2}\) = \(8.63 \times 10^{-5} \,\text{kW} \,\text{per}\, \text{km}^2\)

Calculate the geothermal power passing through the college campus

Now we will find the geothermal power that passes through an area of 1 square kilometer (the typical size of a college campus). Geothermal Power passing through college campus = (Geothermal power density) * (Campus area) Power_College_Campus = \(8.63 \times 10^{-5}\,\text{kW} \cdot 1\,\text{km}^2\) = 0.0863 kW

Convert kW to MW

In order to compare the result with a typical college electrical demand (20 MW), we need to convert the geothermal power passing through the college campus from kW to MW. Power_College_Campus (MW) = \(\frac{0.0863\,\text{kW}}{10^{3}}\) = 8.63 \(\times 10^{-5}\) MW

Compare the geothermal power to the college electrical demand

Now let's compare the geothermal power passing through the college campus to the typical college electrical demand which is 20 MW. Geothermal_Power_Percentage = \(\frac{8.63 \times 10^{-5}\,\text{MW}}{20\,\text{MW}} \times 100\) = 4.315 \(\times 10^{-4} \%\) Based on the comparison, the geothermal power passing through a typical college campus is about 4.315 \(\times 10^{-4}\%\) of the college's electrical demand. This shows that the geothermal power is significantly lower than the typical college's electrical demand.

Key concepts

Geothermal Power Density

The concept of geothermal power density is foundational in understanding the amount of energy available from the Earth's heat. It represents the amount of geothermal power available per unit area of the Earth's surface. In our exercise, this density is calculated by dividing the Earth's total geothermal output, which is 44 terawatts (TW), by its surface area, roughly 510 million square kilometers.

When we perform this calculation, the geothermal power density comes out to be approximately 0.0863 kilowatts per square kilometer. While this figure might seem small, it's crucial to remember that the Earth has a vast surface area, which translates to an immense total geothermal potential. This energy is a result of the natural radioactive decay of elements and the residual heat from the Earth's formation.

Energy Conversion

Understanding energy conversion is essential for comparing different energy sources. The step-by-step solution mentions converting the geothermal power passing through the college campus from kilowatts (kW) to megawatts (MW), since electrical demand is typically described in MW.

One megawatt is equal to 1,000 kilowatts, thus, when we convert 0.0863 kW to MW, we get 8.63 × 10^-5 MW. This conversion is critical for making meaningful comparisons between the geological energy potential and the actual energy requirements, such as those of a college campus. Simplified, the energy conversion process allows us to measure and compare the scales of energy production and consumption across different units.

Educational Energy Demand Comparison

Comparing geothermal energy potential to a college's energy demand puts into perspective the practicability of using geothermal energy to meet real-world needs. In our example, the geothermal power passing through a typical college campus is about 8.63 × 10^-5 MW, which is a fraction of the campus's typical electrical demand of 20 MW.

This comparison reveals that the geothermal energy directly under a college campus is not sufficient to meet its demands, which could include heating, cooling, lighting, and powering electronic devices for educational purposes. It is evident that if a college wishes to rely on geothermal energy, additional resources and technologies would be required to harness energy from a larger area or from deeper within the Earth to meet such significant energy needs.