Question 1

Assume that the historical growth rate of the human population was constant at 1.6% per year. For a population of 7 billion in 2012, determine the time in the past when the human population was 2.

Accepted Answer

As the annual percentage growth rate is small then we can use the approximation
of equation (2.4) to get the doubling time from R so $$t _ { D } = \left( \frac { 100 \ln 2 } { R } \right) = \frac { ( 100 ) \times ( 0.693 ) } { 1.6 } = 43.31 \text { years }$$
from equation (2.7) the constant $a$ can be found to be
$$a = \left( \frac { \ln 2 } { t _ { D } } \right) = \frac { 0.693 } { 43.31 \mathrm { y } } = 0.016 \mathrm { y } ^ { - 1 }$$
from equation (2.4) we start with an initial population of $N _ { 0 } = 2$ at $t = 0$ then $N ( t ) = 6.7 \times 10 ^ { 9 }$ then from
$$N ( t ) = N _ { 0 } \exp ( a t )$$
so
$$t = \frac { 1 } { a } \ln \frac { N ( t ) } { N _ { 0 } } = \frac { 1 } { 0.016 } \ln \frac { 7 \times 10 ^ { 9 } } { 2 } = 1374 \mathrm { y }$$
in the past or at year 2012-1374 $= 638$ (obviously growth rate was not constant)

Question 2

the example of energy use on page 31, leading to equation (2.1), consider a family (two people) who use gasoline at the rate indicated but who heat their home electrically in accordance with the efficiencies given in the text above equation (2.1). How would this affect the per person power consumption?

Accepted Answer

Assuming an efficiency of 40% for electricity generation the primary energy use for two people will be gasoline $9.8 \times 10 ^ { 10 } \mathrm {~J}$
heating $( 1 / 0.4 ) \times \left( 1.04 \times 10 ^ { 11 } \mathrm {~J} \right) = 2.6 \times 10 ^ { 11 } \mathrm {~J}$
electricity (non-heating) $( 1 / 0.4 ) \times \left( 4.32 \times 10 ^ { 10 } \mathrm {~J} \right) = 1.1 \times 10 ^ { 11 } \mathrm {~J}$
Therefore the per capita primary power consumption will be
$$0.5 \times \frac { ( 0.98 + 2.6 + 1.1 ) \times 10 ^ { 11 } \mathrm {~J} } { 3.15 \times 10 ^ { 7 } \mathrm {~s} / \mathrm { y } } = 7.4 \mathrm {~kW}$$
compared to $5.0 \mathrm {~kW}$ for oil heating.

Question 3

A person in the United States consumes 2000 Calories of food per day.
What fraction of the average per capita energy use, as indicated in Table 2.1, does this
represent?

Accepted Answer

From the Table the per capita power consumption is 11,730 W. This represents $$( 11730 \mathrm {~J} / \mathrm { s } ) \times ( 24 \mathrm {~h} / \mathrm { d } ) \times ( 3600 \mathrm {~s} / \mathrm { h } ) = 1.01 \times 10 ^ { 9 } \mathrm {~J} / \mathrm { d }$$
Food consumption represents
$$( 2000 \mathrm { Cal } / \mathrm { d } ) \times ( 4180 \mathrm { Ca } / / \mathrm { J } ) = 8.37 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { d }$$
or
$$100 \times \left( 8.37 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { d } \right) / \left( 1.01 \times 10 ^ { 9 } \mathrm {~J} / \mathrm { d } \right) = 0.83 \% \text { of energy use }$$

Question 4

If a quantity has a doubling time of 30 days and its value is 1000 units at
noontime today, what will be its value at noontime tomorrow?

Accepted Answer

The answer of If a quantity has a doubling time...

Question 5

Assume that the combustion of coal is approximated by the burning of carbon. If a coal-fired generating station operates at 40% efficiency, calculate the amount of CO₂ emitted per MWh of electricity produced.

Accepted Answer

The answer of Assume that the combustion of coal is...

Question 6

Repeat problem 2.15 for the combustion of natural gas (methane). How
does the use of the HHV affect your answer?

Accepted Answer

The answer of Repeat problem 2.15 for the combustion of...

Question 7

For an annual growth rate of 1.6%, use the data in Table 2.3 to estimate the
year in which the human population will reach 200 per km2 of land area.

Accepted Answer

The answer of For an annual growth rate of 1.6%,...

Question 8

The population of a state is 25,600 in the year 1800 and 218,900 in the year 1900. Calculate the expected population in the year 2000 if (a) the growth is linear and (b)the growth is exponential.

Accepted Answer

The answer of The population of a state is 25,600...

Question 9

Consider a solar photovoltaic system with a total rated output of 10 MWe and
a capacity factor of 29%. If the total installation cost is $35,000,000, calculate the decrease in the cost of electricity per kilowatt-hour if the payback period is 25 years instead of 15 years. Assume a constant interest rate of 5.8%.

Accepted Answer

The answer of Consider a solar photovoltaic system with a...

Question 10

The population of a country as a function of time is shown in the following
table. Is the growth exponential? $$\begin{array} { l l } 
\hline \text { year } & \text { population (millions) } \
\hline 1700 & 0.501 \
1720 & 0.677 \
1740 & 0.891 \
1760 & 1.202 \
1780 & 1.622 \
1800 & 2.163 \
1820 & 2.884 \
1840 & 3.890 \
1860 & 5.176 \
1880 & 6.761 \
1900 & 8.702 \
1920 & 10.23 \
1940 & 11.74 \
1960 & 13.18 \
1980 & 14.45 \
2000 & 15.49 \
\hline
\end{array}$$

Accepted Answer

The answer of The population of a country as a...

Question 11

What is the current average human population density (i.e., people per square
kilometer) on earth?

Accepted Answer

The answer of What is the current average human population...

Question 12

The total world population in 2012 was about 7 billion, and Figure 2.11 shows that at that time the actual world population growth rate was about 1% per year. The figure also shows an anticipated roughly linear decrease in growth rate that extrapolates to zero growth in about the year 2080. Assuming an average growth rate of 0.5% between 2012 and 2080, what would the world population be in 2080? How does this compare with estimates discussed in the text for limits to human population?

Accepted Answer

The answer of The total world population in 2012 was...

Question 13

(a) If the total amount of a resource available is $$10 ^ { 10 } \mathrm {~kg} ,$$ calculate its 
lifetime if the rate of use is constant at $10 ^ { 8 } \mathrm {~kg} / \mathrm { y }$.
(b) Repeat part (a) if the initial rate of use is $10 ^ { 8 } \mathrm {~kg} / \mathrm { y }$ and this increases at an annual rate of $5 \%$.
(c) Repeat part (b) for an initial rate of $10 ^ { 8 } \mathrm {~kg} / \mathrm { y }$ and an increase of $10 \%$ per year.

Accepted Answer

The answer of (a) If the total amount of a...

Question 14

Consider an island with a current population density of 50 people/km2 (about equal to the present world average). If the annual growth rate is 2%, determine the year in which the population density be equal to 20,000 people/km2 (approximately the population density of Macau, the world's most densely populated nation).

Accepted Answer

The answer of Consider an island with a current population...

Question 15

If world energy use increases linearly, use Figure 2.13 to estimate the annual percentage increase for OECD and non-OECD countries from 1990 to 2035 relative to the use in 1990.

Accepted Answer

The answer of If world energy use increases linearly, use...

Question 16

A quantity has a doubling time of 110 years. Estimate the annual percent
increase in the quantity.

Accepted Answer

The answer of A quantity has a doubling time of...

Question 17

(a) Assume that human population growth is described as exponential growth and the current population is 7.5 billion. If the current daily increase in population is 250,000, calculate the doubling time.
(b) For the conditions in part (a), what is the current annual growth rate?

Accepted Answer

The answer of (a) Assume that human population growth is...

Question 18

If a facility has a capital recovery factor of 0.12 and the annual interest rate
is 5%, what is the payback period?

Accepted Answer

The answer of If a facility has a capital recovery...

Question 19

The population of a particular country has a doubling time of 45 years. When
will the population be three times its present value?

Accepted Answer

The answer of The population of a particular country has...

Question 20

From the data in Table 2.1 and Figure 2.3, estimate the total energy
production per year from hydroelectricity in the United States.

Accepted Answer

The answer of From the data in Table 2.1 and...

Quiz 2: Past, Present, and Future World Energy Use

Assume that the historical growth rate of the human population was constant at 1.6% per year. For a population of 7 billion in 2012, determine the time in the past when the human population was 2.

A person in the United States consumes 2000 Calories of food per day. What fraction of the average per capita energy use, as indicated in Table 2.1, does this represent?

If a quantity has a doubling time of 30 days and its value is 1000 units at noontime today, what will be its value at noontime tomorrow?

Assume that the combustion of coal is approximated by the burning of carbon. If a coal-fired generating station operates at 40% efficiency, calculate the amount of CO2 emitted per MWh of electricity produced.

Repeat problem 2.15 for the combustion of natural gas (methane). How does the use of the HHV affect your answer?

For an annual growth rate of 1.6%, use the data in Table 2.3 to estimate the year in which the human population will reach 200 per km2 of land area.

The population of a state is 25,600 in the year 1800 and 218,900 in the year 1900. Calculate the expected population in the year 2000 if (a) the growth is linear and (b)the growth is exponential.

What is the current average human population density (i.e., people per square kilometer) on earth?

If world energy use increases linearly, use Figure 2.13 to estimate the annual percentage increase for OECD and non-OECD countries from 1990 to 2035 relative to the use in 1990.

A quantity has a doubling time of 110 years. Estimate the annual percent increase in the quantity.

(a) Assume that human population growth is described as exponential growth and the current population is 7.5 billion. If the current daily increase in population is 250,000, calculate the doubling time. (b) For the conditions in part (a), what is the current annual growth rate?

If a facility has a capital recovery factor of 0.12 and the annual interest rate is 5%, what is the payback period?

The population of a particular country has a doubling time of 45 years. When will the population be three times its present value?

From the data in Table 2.1 and Figure 2.3, estimate the total energy production per year from hydroelectricity in the United States.

Assume that the combustion of coal is approximated by the burning of carbon. If a coal-fired generating station operates at 40% efficiency, calculate the amount of CO₂ emitted per MWh of electricity produced.