Chapter 22, Problem 3EFA

To determine

The reduction in percentage and the average distance driven that to reduce the annual carbon footprint calculated in Question 1 by half.

Answer to Problem 3EFA

The number of cars have to be reduced by 50 % or the average kilometers that a car be driven in one year have to be reduced to 10,000 km to reduce the annual carbon footprint calculated in Question 1 by half.

Explanation of Solution

Given info:

From Question 1, the carbon footprint per car produced by one car in a year is about 4 metric tons or 4,000 kg per year if on an average, it is driven 20,000 km in one year; at such a rate and assuming the total number of cars in the city to be 7 million, about 28 million metric tons (28,000,000 metric tons) of carbon dioxide is produced in a year.

It is given that an internal combustion engine in a car releases approximately 200 grams (0.2 kilograms or 0.44 pounds) of CO₂ per kilometer if it is driven under normal driving conditions. Now, the approximate amount of CO₂ released from a car engine cannot change all of a sudden. However, in order to bring down the annual emission of CO₂ from a car, the kilometers it is being driven have to be reduced. The value for CO₂ released from a car engine was obtained in Question 1 as 4000 kg/ yr. Half of this value is 2000 kg/yr

In Question 1, carbon dioxide released by the engine of a car in one year if it is driven on an average of 20,000 kilometers a year was calculated using the expression given below:

$\left(\begin{array}{l}{\text{CO}}_2\text{ released by the engine}\\ \text{ of a car in one year}\end{array}\right)=\left(\begin{array}{l}{\text{CO}}_2\text{ released by the engine }\\ \text{of a car per kilometer}\end{array}\right)\times \left(\begin{array}{l}\text{Number of kilometers the car }\\ \text{was driven in one year}\end{array}\right)$

The reduction in the average car driven distance can be calculated by replacing the value for CO₂ released by the engine of a car in one year with 2000 kg instead of 4000 kg and rearranging the above expression as given below:

$\left(\begin{array}{l}\text{Number of kilometers the car }\\ \text{can be driven in one year}\end{array}\right)=\frac{\left(\begin{array}{l}{\text{CO}}_2\text{ released by the engine}\\ \text{ of a car in one year}\end{array}\right)}{\left(\begin{array}{l}{\text{CO}}_2\text{ released by the engine }\\ \text{of a car per kilometer}\end{array}\right)}$

Substitute 0.2 kg for the CO₂ released by the engine of a car per kilometer and 2000 kg for CO₂ released by the engine of a car in one year in the above expression to obtain the number of kilometers the car can be driven in one year to reduce the CO₂ emission by half the value obtained in Question 1.

$\begin{array}{c}\left(\begin{array}{l}\text{Number of kilometers the car }\\ \text{can be driven in one year}\end{array}\right)=\frac{\left(2000\text{ kg}\right)}{\left(0.2\text{ kg}\right)}\\ =10,000\text{ km}\end{array}$

Hence, to reduce the annual carbon footprint calculated in Question 1 by half, the number of kilometers a car is driven annually on an average have to be reduced to 10, 000 km from 20,000 km, which means the number of kilometers were also reduced by 50%.

In Question 1, the total number of metric tons of CO₂ that is produced by all the cars in the city in 1 year was be obtained using the given expression:

$\left(\begin{array}{l}\text{Total number of metric tons}\\ {\text{ of CO}}_{\text{2}}\text{ that are produced by all}\\ \text{ the cars in the city during 1 year}\end{array}\right)=\left(\begin{array}{l}\text{No}{\text{. of metric tons of CO}}_{\text{2}}\\ \text{released by the engine}\\ \text{ of a car in one year}\end{array}\right)\times \left(\begin{array}{l}\text{Total number of cars }\\ \text{driven in the city}\end{array}\right)$

As of Question 1, the total number of metric tons of CO₂ that is produced by all the cars, assumed as 7 million, in the city in 1 year was obtained as 28,000,000 metric tons when the number of metric tons of CO₂ released by the engine of a car in one year was 4 metric tons.

Now, in order to reduce the value of CO₂ released by cars in one year by half the value obtained in Question 1 (that is, half of 28,000,000, which is 14,000,000), keep the value of CO₂ released by the engine of a car per year to be 4 metric tons itself; the above expression can be rearranged along with the replacement of some values. The equation then becomes as follows:

$\left(\begin{array}{l}\text{Total number of cars }\\ \text{driven in the city}\end{array}\right)=\frac{\left(\begin{array}{l}\text{Total number of metric tons}\\ {\text{ of CO}}_{\text{2}}\text{ that are produced by all}\\ \text{ the cars in the city during 1 year}\end{array}\right)}{\left(\begin{array}{l}\text{No}{\text{. of metric tons of CO}}_{\text{2}}\\ \text{released by the engine}\\ \text{ of a car in one year}\end{array}\right)}$

Substitute 14,000,000 for the total number of metric tons of CO₂ that is produced by all the cars in the city in 1 year and 4 metric tons for the number of metric tons of CO₂ released by the engine of a car in one year in the above expression to reduce the CO₂ emission from all the cars in the city by half the value obtained in Question 1.

$\begin{array}{c}\left(\begin{array}{l}\text{Total number of cars }\\ \text{driven in the city}\end{array}\right)=\frac{\left(\text{14,000,000}\right)}{\left(\text{4 metric tons}\right)}\\ =\text{3,500,000}\end{array}$

Hence, to reduce the annual carbon footprint calculated in Question 1 by half, the number of cars that can be driven annually has to be reduced from 7 million to 3.5 million, which means the number of cars have to be reduced by 50%.