Summary of "Volcano trash math. #math #maths #mathematics #science #stem #facts #interesting #interestingfacts"

Summary of "Volcano trash math"

This video explores the idea of disposing of the world’s trash by throwing it into volcanoes and explains why this is not a feasible solution using mathematical and scientific reasoning.

Main Ideas and Concepts

Global Trash Production:
- The world produces approximately 2.01 billion tons of municipal solid waste annually.
- Average trash density worldwide is about 300 kg/m³ (higher in lower-income countries).
Calculating Trash Volume:
- Total volume of trash generated yearly is around 6.7 cubic kilometers (mass ÷ density).
Volcano Capacity for Trash Disposal:
- There are about 1,500 active volcanoes globally.
- Only a few shield volcanoes have open lava lakes suitable for trash disposal:
  - Mount Nongo (Democratic Republic of Congo)
  - Kilauea (Hawaii)
  - Erta Ale (Ethiopia)
  - Masaya (Nicaragua)
- Many other volcanoes are inaccessible or unsuitable.
- Example: Mount Nongo has a crater volume of 0.126 cubic km, which is less than 2% of the total annual trash volume.
Local Waste Disposal Case Study (Goma, near Mount Nongo):
- Goma’s population: ~1 million people, generating 700 tons of waste daily.
- With a trash density of 250 kg/m³, daily trash volume is about 2,800 m³.
- The volcano’s crater could theoretically hold 123 years of Goma’s trash.
Challenges with Trash Composition and Energy Requirements:
- Food waste contains 55-70% water; plastics/rubber ~2%.
- Effective average water content in Goma’s waste is about 60%.
- To evaporate water in the trash, the volcano must supply significant energy:
  - Specific heat of water: 4,186 J/kg°C
  - Latent heat of vaporization: 2.2 million J/kg
  - Total energy needed to heat and vaporize water per kg: ~2.6 million J
- For daily water content in trash, energy requirement is about 1 terajoule per day.
Energy Limitations of Lava:
- Lava energy is approximately 1.7 gigajoules per cubic meter.
- This means 630 m³ of lava would solidify daily due to cooling from trash, forming a crust.
- The crust would block further trash disposal, making the volcano unusable for this purpose.
Conclusion:
- Throwing trash into volcanoes is impractical due to limited volume capacity and insufficient energy to vaporize the water content in the trash.
- The crust formation on lava lakes further prevents continuous trash disposal.

Methodology / Calculations Presented

Trash volume calculation:
Volume = Mass of trash ÷ Density of trash = (2.01 × 10⁹ tons) ÷ (300 kg/m³) ≈ 6.7 km³
Volcano crater volume (example Mount Nongo):
Volume = π × (800/2)² × 250 ≈ 0.126 km³
Daily trash volume for Goma:
700 tons/day = 700,000 kg/day Volume = 700,000 ÷ 250 = 2,800 m³/day
Energy required to vaporize water in trash:
Energy per kg = Specific heat × ΔT + Latent heat ≈ 2.6 × 10⁶ J/kg
Total energy per day:
Energy = 420,000 kg water × 2.6 × 10⁶ J/kg ≈ 1 terajoule
Lava solidification rate:
Energy per m³ = 1.7 × 10⁹ J Volume solidified = (1 × 10¹² J) ÷ (1.7 × 10⁹ J/m³) ≈ 630 m³