Emissions Control:

Analyzing the Environmental Impact


An important equation to analyze environmental problems:

I=PAT (1)

where I=impact


A=in loose terms, affluence


Affluence, also known as wealth, is a stock (e.g., how much one owns). Consumption is a flow (e.g., how much one consumes or acquires per unit time). Equation (1) can be written in terms of either stock or flow.


For example, the fuel used by all the cars in the United States may be thought of as a compounding of the human population, the number of cars per capita, and the fuel use per car:

Fuel use=(Population)(Number of cars per capita)(Fuel use per car)


There are at least three reasons to analyze environmental problems using I=PAT

1. It shows how contributing factors compound to produce a total effect.

2. It allows assignment of blame or praise to important factors

3. It guides access for policy and action.





The factors PAT are not the only possible in this generic approach. We can break each factor in several sub-factors. For example, in exploring the CO2 emissions we can use four factors:

CO2=(Population)(Consumption of economic goods and services)

x(Energy per unit of economic goods and services)

x(CO2 per unit of energy)


or more simply:

CO2=(Population)(Consumption/Person)(Energy/Consumption unit) x(CO2/Energy)


A self-consistent set of units is

(tons/year)=(persons)(dollars/(person * year)(joules/dollar)(tons/joule)



If we want to investigate the C emissions worldwide here is how we can do this:

C released(Population)(Economic production per capita)

x(C per unit of economic production)


Table 1.1 covers world carbon emissions resulting directly from fossil fuel combustion which is approximately 3/5 of all carbon emissions.








Table 1.1 World Fuel-Related Carbon Emissions and Economic Product, 1960-1990






Human Population


Gross Economic Product per Capita [$(1987)/person year]*

Carbon per Unit of Economic Product [Kg C/$(1987)]

World Carbon Release

(1012 Kg C/year)





















*Monetary data are given in constant 1987 dollars, indicated as $(1987)

Source: Data from Brown et al. (1993), pp. 61, 73



1. Can you use these data to analyze the components of growth for the three decades 1960-1990? (Hint: Divide the 1970 equation by the 1960 equation of I=PAT Calculate this for all three decades and compare them) What does this say for the world carbon releases?


2. Can you form a similar table for CO2 to estimate the CO2 emissions in DuPage county?

Here are the four factors you can use:


3. Compare the above method of calculating the CO2 emissions with the method described below in which you estimate the CO2 emissions using the data from TCD. What are the advantages and disadvantages of each method?



In this activity you will compute the amount of carbon dioxide produced in pounds by the vehicles on which the emissions test has been performed (You can access the emissions database at the following site:


Plot the carbon dioxide measurements on the Y axis and cars on the X axis to show the carbon dioxide pollution trend in these cars. Use the following sample calculation (You are reminded that 1 mile=1.609 km, 1 gallon=3.785 l, and 1 pound=.453 kg) to find

the amount of carbon dioxide produced in pounds by the vehicles.


Sample calculation:


miles traveled by the car=2700 miles

gas consumed=2000 miles/30 mpg=90 gallon gas

Carbon Dioxide produced=(20 lbs Carbon Dioxide/gallon) x (90 gallons)= 1800 lbs


Carbon dioxide (this is only for one car!). You can calculate also (on the average) how much Carbon Dioxide is produced by this car in a year/month/week. How? Think about this.


To do these calculations, you can assume that:

the average car gets 30 miles per gallon, or you can find the exact carís gas mileage in miles per gallon (mpg) for each of the cars they have tested.

approximately 20 pounds (9 kg) of Carbon Dioxide are produced per gallon consumed

the average young tree removes 25 pounds (11.3 kg) of Carbon Dioxide per year.


The above graph you have made shows how much carbon dioxide each car contributes to the atmosphere each year. Can you estimate the amount of carbon dioxide produced in DuPage county? For the past year? For the past five years? How? Can you estimate the amount of carbon dioxide in your county for the next five years?



4. Using the above information plan a strategy to reduce the auto mileage for the cars involved in the emissions tests. For example, can you reduce by 1000 pounds the amount of Carbon Dioxide these cars put into the atmosphere each year? How? Suggest specific ways to the people who have the cars how they can do that. In addition to consuming less gas, you can also plant trees. For example, by planting 10 trees a year, your family could remove 250 pounds of Carbon dioxide from the atmosphere. Given that an average forest has about 400 trees per acre, can you figure out how many acres of forest must be planted in your community to absorb the amount of Carbon Dioxide that these cars produce (on the average) every year?


5. Can you estimate the growth in CO2 emissions in DuPage county in 2050? How?




Herendeen, R. A. (1998). Ecological numeracy: Quantitative analysis of environmental issues. New York: John Wiley & Sons