micha

Quantitative Reasoning – Global Warming

Micha Tomkiewicz, Physics

The Environmental Studies Program

 

The presentation explores mandating two tiers of Quantitative Reasoning (QR) intensive courses at Brooklyn College: All students admitted to Brooklyn College will take a BC assessment test in QR that will include the following “Math Tool Kit”:

 

 

Students who pass the test will be required to take at least one more designated QR course.  Students who fail the assessment test will be offered extensive tutoring in Math and will be required to take a designated freshman QR course. Students will be able to choose among various topics such as:

 

  • QR – Global Warming
  • QR – Creation (Astronomy)
  • QR – Financial Markets
  • QR – Statistics in Sport

 

Each QR course will constitute about 40% of the Math Tool Box and 60% of the subject matter for the course. Students will be tested separately on the Math Tool Box part and on the course material.

 

In what will follow we will concentrate on QR-Global Warming. We will provide an outline of the proposed syllabus and a sample of a lecture that creates a very simple model of the energy content of the Amazon forest, compares it with the total global energy use and tries to determine whether the numbers support a position that our CO2 producing energy use is significant compared to the ability of the planet to sequestrate  CO2.

 

Proposed Syllabus:

 

QR – Global Warming

 

•         Whom to believe – Methods for finding the “truth” individually and collectively:

–        The Scientific Method

•         Reasoning:

–        Deduction

–        Induction

–        Hypothesis Building

–        Importance of data

v      Quality of data

–        Appeal to Authority

–        Advocacy Systems

•         The Issue – Do we have an environmental problem?

–        Population Trends and the “Noble Savage”.

•         Exponential growth

–         Comparison of the Amazon forest growth with the global annual energy use

•         Modeling

•         Chemistry

•         Scientific notation

•         Geometry

•         The Data:

–        Average global temperature over the last 100 years

–        Average CO2 emission over the last 100 years

–        Energy use per capita vs. GDP/Capita – Standard of Living.

•         The Science – Radiation

–        Blackbody Radiation

–        Earth energy balance

–        Estimate of global average temperature

–        Greenhouse effect

–        Greenhouse gases

•         Model building

•         Working with formulas

 

 

•         The Science – Energy

–        Photosynthesis

–        Respiration

–        Laws of Thermodynamics

–        Energy from fossil fuels

–        Energy conversion

•         The Tradeoffs – Economy and Politics

•         Advance Warnings

 

 

 

 

The Model:

 

 


Text Box: A Simple Model to Estimate the Energy Content of the Amazon Forest Single Tree: Assume: 20m height; 0.5m diameter; density = 0.7 gm/cm3 (Indian teak) Weight of the tree: = volume x density Volume: = base*height = (assume square base) (50cm)2*2000cm = 5X106 cm3 Weight: = (5X106 cm3)*(0.7 gm/cm3) = 3.5X106 g = 3.5 tons Sugar ≡ cellulose ≡ (HCOH)n Fraction of Carbon: = 12/(12+2+16) = 0.4 = 40% Amount of Carbon in each Tree: = 3.5X0.4 = 1.4tons = 1.4X106g Amazon Rain Forest: Area: = 2.7X106 miles2 = 7.5X106 km2 Assume: space between trees = 10m Number of trees in the Forest: = area/(area/tree) = 7.5X1012m2/100m2 = 7.5X1010 trees (75 Billion). Total Amount of Carbon in the Rain Forest = number of trees X amount of carbon/tree = 7.5X1010 X 1.4 tons/tree = 1 X 1011 tons of carbon Amount of Energy Released by complete Burning of the Forest = total carbon X energy/gm C = (1 X 1011 tons) X (106 g/ton) * (210 kcal/ 12 g of C) = 1.8X1018 kcal = 7.1 X 1018 BTU (1BTU = 0.252 Kcal)

 

 

 

 

 

 

 

 

Energy for Life – with a little bit of Chemistry

 

Photosynthesis:

6CO2 + 6H2O   C6H12O6 + 6O2

 

Respiration

 

C6H12O6 + 6O2              6CO2 + 6H2O   + biologically stored energy

 

Burning of Fossil Fuel:

 

 

                 CH4 (main constituent of natural gas)   +  2O2     CO2 + 2H2O   + energy

 

Energy/mole = 210kcal/mole = 210 Kcal/(12g carbon)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 


Total Energy Consumption of Carbonated

Fossil Fuel in 1993= 3X1017 BTU

= 4.2% of the Forest/year

 

Real Data:Text Box: The issue that caught the attention of everybody and took about half of the discussion time was the assumption that the base of the trees is square. Let's examine this assumption: The figure below shows a circle in a square: The side of the square and the diameter of the circle are equal. Let's designate them with the letter d. The radius of the circle is half its diameter – let's designate it with the letter r. d = 2*r The area of the square is d2 = (2*r)2 = 4r2 The area of the circle is πr2 where π = 3.14 to a very good approximation. The ratio of the area of the square to that of the circle is 4r2/ πr2 = 1.27 The error in representing the base of the trees as squares instead of circles amounts to 27%. Very small compared to the other approximations in the model.