Question 1

Liquid natural gas is transported by ship. A typical LNG tanker may have a capacity of $10 ^ { 5 } \mathrm {~m} ^ { 3 }$. If this fuel is used to provide energy for a city with a population of 1 million and each person consumes power at an average rate of $10 \mathrm {~kW}$, how long would the LNG last?

Accepted Answer

From the text the volume of LNG is 1/600 that of the volume of the same amount of natural gas. Natural gas has an energy density of 3.85×107 J/m3 at STP so LNG will have an energy density of $$( 600 ) \times \left( 3.85 \times 10 ^ { 7 } \mathrm {~J} / \mathrm { m } ^ { 3 } \right) = 2.31 \times 10 ^ { 10 } \mathrm {~J} / \mathrm { m } ^ { 3 }$$
The energy content of the fuel carried by the tanker will be
$$\left( 10 ^ { 5 } \mathrm {~m} ^ { 3 } \right) \times \left( 2.31 \times 10 ^ { 10 } \mathrm {~J} / \mathrm { m } ^ { 3 } \right) = 2.31 \times 10 ^ { 15 } \mathrm {~J}$$
Total power consumption for the city will be
$$\left( 10 ^ { 6 } \right) \times \left( 10 ^ { 4 } \mathrm {~W} \right) = 10 ^ { 10 } \mathrm {~W}$$
So the energy provided by the tanker will last
$$\left( 2.31 \times 10 ^ { 15 } \mathrm {~J} \right) / \left( 10 ^ { 10 } \mathrm {~J} / \mathrm { s } \right) = 2.31 \times 10 ^ { 5 } \mathrm {~s} = 64 \text { hours }$$

Question 2

On land, coal is transported primarily by train. A typical large coal train may
be about 1.5 km long and may consist of 120 cars, each holding 110 tonnes of coal. As each tonne of coal has an equivalent energy content (in terms of the stored chemical energy it contains), a moving coal train represents a flow of (chemical) energy or a power. For acoal train traveling at 100 km/h, calculate the equivalent power in watts.

Accepted Answer

One tonne of coal has energy content of $$3.1 \times 10 ^ { 10 } \mathrm {~J}$$ The total amount of coal on
the train is 120×110 tonnes = 13,200 tonnes. This has an energy content of $$( 13,200 \text { tons } ) \times \left( 3.1 \times 10 ^ { 10 } \mathrm {~J} / \text { ton } \right) = 4.09 \times 10 ^ { 14 } \mathrm {~J} \text {. }$$
$100 \mathrm {~km} / \mathrm { h }$ corresponds to
$$( 100 \mathrm {~km} / \mathrm { h } ) \times ( 1000 \mathrm {~m} / \mathrm { km } ) / ( 3600 \mathrm {~s} / \mathrm { h } ) = 27.8 \mathrm {~m} / \mathrm { s }$$
A $1.5 - \mathrm { km }$ long train will pass a reference point in
$$( 1500 \mathrm {~m} ) / ( 27.8 \mathrm {~m} / \mathrm { s } ) = 54 \mathrm {~s}$$
Thus the rate of flow of energy is
$$\frac { 4.09 \times 10 ^ { 14 } \mathrm {~J} } { 54 \mathrm {~s} } = 7.57 \times 10 ^ { 12 } \mathrm {~W} = 7.57 \times 10 ^ { 6 } \mathrm { MW }$$

Question 3

Write down the chemical formulae for the combustion of the alkanes in Table $$3.2 \text { with } n = 2 \text { to } n = 8 \text {. Determine the mass of } \mathrm { CO } _ { 2 } \text { produced per megajoule of energy. }$$

Accepted Answer

The oxidation process is shown below \[\begin{array} { l l l l } 
\hline n & \text { name } & \text { formula } & \text { combustion reaction } \
\hline 2 & \text { ethane } & \mathrm { C } _ { 2 } \mathrm { H } _ { 6 } & 2 \mathrm { C } _ { 2 } \mathrm { H } _ { 6 } + 7 \mathrm { O } _ { 2 } \rightarrow 4 \mathrm { CO } _ { 2 } + 6 \mathrm { H } _ { 2 } \mathrm { O } \
3 & \text { propane } & \mathrm { C } _ { 3 } \mathrm { H } _ { 8 } & \mathrm { C } _ { 3 } \mathrm { H } _ { 8 } + 5 \mathrm { O } _ { 2 } \rightarrow 3 \mathrm { CO } _ { 2 } + 4 \mathrm { H } _ { 2 } \mathrm { O } \
4 & \text { butane } & \mathrm { C } _ { 4 } \mathrm { H } _ { 10 } & 2 \mathrm { C } _ { 4 } \mathrm { H } _ { 10 } + 13 \mathrm { O } _ { 2 } \rightarrow 8 \mathrm { CO } _ { 2 } + 10 \mathrm { H } _ { 2 } \mathrm { O } \
5 & \text { pentane } & \mathrm { C } _ { 5 } \mathrm { H } _ { 12 } & \mathrm { C } _ { 5 } \mathrm { H } _ { 12 } + 8 \mathrm { O } _ { 2 } \rightarrow 5 \mathrm { CO } _ { 2 } + 6 \mathrm { H } _ { 2 } \mathrm { O } \
6 & \text { hexane } & \mathrm { C } _ { 6 } \mathrm { H } _ { 14 } & 2 \mathrm { C } _ { 6 } \mathrm { H } _ { 14 } + 19 \mathrm { O } _ { 2 } \rightarrow 12 \mathrm { CO } _ { 2 } + 14 \mathrm { H } _ { 2 } \mathrm { O } \
7 & \text { heptane } & \mathrm { C } _ { 7 } \mathrm { H } _ { 16 } & \mathrm { C } _ { 7 } \mathrm { H } _ { 16 } + 11 \mathrm { O } _ { 2 } \rightarrow 7 \mathrm { CO } _ { 2 } + 8 \mathrm { H } _ { 2 } \mathrm { O } \
8 & \text { octane } & \mathrm { C } _ { 8 } \mathrm { H } _ { 18 } & 2 \mathrm { C } _ { 8 } \mathrm { H } _ { 18 } + 25 \mathrm { O } _ { 2 } \rightarrow 16 \mathrm { CO } _ { 2 } + 18 \mathrm { H } _ { 2 } \mathrm { O } \
\hline
\end{array}\] The number of moles of $\mathrm { CO } _ { 2 }$ produced per mole of alkane is clearly shown. The molecular mass of the alkane is shown below. The molecular mass $( M )$ of $\mathrm { CO } _ { 2 } ( 44 \mathrm {~g} / \mathrm { mol } )$ can be used to determine the relative mass of $\mathrm { CO } _ { 2 }$ produced per unit mass of alkane. The heat of combustion is given in Table $3.2$ and the amount of $\mathrm { CO } _ { 2 }$ per $\mathrm { MJ }$ heat is found.
$\begin{array}{llllll}
\hline n & \begin{array}{l}
R=(\text { moles } \
\left.\mathrm{CO}_{2}\right) /(\text { moles } \
\text { alkane) }
\end{array} & \begin{array}{l}
M \
\text { (alkane) }
\end{array} & \begin{array}{l}
R \times 44 / M= \
\left(\mathrm{kg} \mathrm{CO}_{2}\right) /(\mathrm{kg} \text { alkane) }
\end{array} & \begin{array}{l}
\text { heat of } \
\text { combustion } \
\mathrm{MJ} / \mathrm{kg}
\end{array} & \mathrm{kg}\left(\mathrm{CO}_{2}\right) / \mathrm{MJ} \
\hline 2 & 2 & 30 & 2.93 & 51.9 & 0.0565 \
3 & 3 & 44 & 3.00 & 50.3 & 0.0596 \
4 & 4 & 58 & 3.03 & 49.5 & 0.0612 \
5 & 5 & 72 & 3.06 & 48.7 & 0.0628 \
6 & 6 & 86 & 3.07 & 48.1 & 0.0638 \
7 & 7 & 100 & 3.08 & 48.1 & 0.0640 \
8 & 8 & 114 & 3.09 & 46.8 & 0.0660 \
\hline
\end{array}$

Question 4

Locate the current world price of oil (US$/bbl), coal (bituminous coal, per tonne), and natural gas (per1000 m³). For each fossil fuel, calculate the cost of energy pergigajoule assuming that the fuel can be converted to usable energy with an efficiency of 100%.

Accepted Answer

The answer of Locate the current world price of oil...

Question 5

(a) Locate, from an appropriate source, the composition for methanol and ethanol. Write down the formulas for the combustion of these two hydrocarbons. (b) Calculate the mass of CO₂ produced per kg of methanol and ethanol burned. (c) Locate values for the heat of combustion of methanol and ethanol and determine the mass of CO₂ produced per MJ of energy.

Accepted Answer

The answer of (a) Locate, from an appropriate source, the...

Question 6

A coal-fired generating station consumes 2 × 106 tonnes of coal per year and
produces an average electrical output of 800 MWe. Calculate the plant's efficiency.

Accepted Answer

The answer of A coal-fired generating station consumes 2 ×...

Question 7

Find the retail cost of gasoline (per unit volume) in your area and find the
cost of electricity for residential users in your area.
(a) Compare the cost of energy (per MJ) from gasoline and from electricity from the public utility.
(b) The efficiency of a gasoline automobile is about 20% and the efficiency of a battery electric vehicle is about 85%. Discuss the relative transportation costs for gasoline and electric vehicles.

Accepted Answer

The answer of Find the retail cost of gasoline (per...

Question 8

A large passenger ship weighs 75,000 tonnes and has a cruising speed of 45 km/h. The engines burn diesel fuel (approximately the same energy content as crude oil) with an efficiency of 20%. The drive system has an average efficiency of 55% for converting mechanical energy into propulsion for the ship. Calculate the volume of fuel needed to accelerate the ship from rest to cruising speed.

Accepted Answer

The answer of A large passenger ship weighs 75,000 tonnes...

Question 9

For the reaction shown in equation (3.4), calculate the mass of CO and the mass of H₂ produced by the gasification of 1 kg of carbon. What is the energy content of these two products?

Accepted Answer

The answer of For the reaction shown in equation (3.4),...

Question 10

A coal-fired generating station has an efficiency of 38% and produces an
average electrical output of 1000 MWe.
(a) How much coal does it burn per second? Assume the coal is bituminous.(b) How much heat (in joules) is released to the environment per second?
(c) How many liters of water at 20°C could the heat in part (b) boil (at STP) per second?

Accepted Answer

The answer of A coal-fired generating station has an efficiency...

Question 11

How many tonnes of oil shale which produces 120 L/t would be needed to
produce the same energy as 1 tonne of bituminous coal?

Accepted Answer

The answer of How many tonnes of oil shale which...

Question 12

Assume that all of the United States' annual electricity requirement of 3×1012 kWh is produced by coal-fired generating stations operating at a net overall efficiency of 40%. (a) How many tonnes of coal are burned per second? (Assume the coal is all bituminous) (b) Assuming that coal is 100% carbon, how many tonnes of CO₂ will be produced each year?

Accepted Answer

The answer of Assume that all of the United States'...

Question 13

The combustion of pure hydrogen by the reaction $$2 \mathrm { H } _ { 2 } + \mathrm { O } _ { 2 } \rightarrow 2 \mathrm { H } _ { 2 } \mathrm { O }$$ produces $142 \mathrm { MJ }$ per kg of hydrogen. Compare the energy per kg of octane and the total energy from the individual combustion of its carbon and hydrogen atoms.

Accepted Answer

The answer of The combustion of pure hydrogen by the...

Question 14

A person uses the energy equivalent of 50 bbl of crude oil in one year. What
is that person's average power consumption?

Accepted Answer

The answer of A person uses the energy equivalent of...

Question 15

Assume that the total energy needs of a person in the United States (Chapter
2) is satisfied by burning coal. If each person is responsible for the mining, transportation, processing, and burning of their own coal, how much coal must each person process, on average, per day?

Accepted Answer

The answer of Assume that the total energy needs of...

Question 16

A portion of the Keystone Pipeline connecting oil production in Canada and
refining in the United States consists of a 0.76 m diameter pipe that carries 500,000 bbl of crude oil per day over a distance of 1744 km.
(a) Calculate the average velocity of the oil in the pipe.
(b) What is the rate of chemical energy flow through the pipe (in watts) based on the velocity of the oil and its energy content?

Accepted Answer

The answer of A portion of the Keystone Pipeline connecting...

Question 17

Locate the current world price of oil (US$/bbl) and the current retail price of regular gasoline in your area (per liter or per gallon, as appropriate). What is the markup in the price per unit energy between crude oil and retail gasoline?

Accepted Answer

The answer of Locate the current world price of oil...

Question 18

Using the information in Figure 2.6 and the average composition of coal
(lignite, sub-bituminous/bituminous and anthracite) in the United States, calculate the mass of the coal used annually. Use the average energy content for sub-bituminous/bituminous coal.

Accepted Answer

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Question 19

Estimate the total coal produced in the United Kingdom between 1820 and
the present.

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Question 20

If shale oil replaced coal in the United States, how many years would the
U.S. resources last at the current rate of use?

Accepted Answer

The answer of If shale oil replaced coal in the...

Exam 3: Fossil Fuel Resources and Use

Write down the chemical formulae for the combustion of the alkanes in Table $3.2 \text { with } n = 2 \text { to } n = 8 \text {. Determine the mass of } \mathrm { CO } _ { 2 } \text { produced per megajoule of energy. }$

Locate the current world price of oil (US$/bbl), coal (bituminous coal, per tonne), and natural gas (per1000 m³). For each fossil fuel, calculate the cost of energy pergigajoule assuming that the fuel can be converted to usable energy with an efficiency of 100%.

A coal-fired generating station consumes 2 × 106 tonnes of coal per year and produces an average electrical output of 800 MWe. Calculate the plant's efficiency.

For the reaction shown in equation (3.4), calculate the mass of CO and the mass of H₂ produced by the gasification of 1 kg of carbon. What is the energy content of these two products?

How many tonnes of oil shale which produces 120 L/t would be needed to produce the same energy as 1 tonne of bituminous coal?

A person uses the energy equivalent of 50 bbl of crude oil in one year. What is that person's average power consumption?

Assume that the total energy needs of a person in the United States (Chapter 2) is satisfied by burning coal. If each person is responsible for the mining, transportation, processing, and burning of their own coal, how much coal must each person process, on average, per day?

Locate the current world price of oil (US$/bbl) and the current retail price of regular gasoline in your area (per liter or per gallon, as appropriate). What is the markup in the price per unit energy between crude oil and retail gasoline?

Using the information in Figure 2.6 and the average composition of coal (lignite, sub-bituminous/bituminous and anthracite) in the United States, calculate the mass of the coal used annually. Use the average energy content for sub-bituminous/bituminous coal.

Estimate the total coal produced in the United Kingdom between 1820 and the present.

If shale oil replaced coal in the United States, how many years would the U.S. resources last at the current rate of use?

Exam 3: Fossil Fuel Resources and Use

Locate the current world price of oil (US$/bbl), coal (bituminous coal, per tonne), and natural gas (per1000 m3). For each fossil fuel, calculate the cost of energy pergigajoule assuming that the fuel can be converted to usable energy with an efficiency of 100%.

A coal-fired generating station consumes 2 × 106 tonnes of coal per year and produces an average electrical output of 800 MWe. Calculate the plant's efficiency.

For the reaction shown in equation (3.4), calculate the mass of CO and the mass of H2 produced by the gasification of 1 kg of carbon. What is the energy content of these two products?

How many tonnes of oil shale which produces 120 L/t would be needed to produce the same energy as 1 tonne of bituminous coal?

A person uses the energy equivalent of 50 bbl of crude oil in one year. What is that person's average power consumption?

Assume that the total energy needs of a person in the United States (Chapter 2) is satisfied by burning coal. If each person is responsible for the mining, transportation, processing, and burning of their own coal, how much coal must each person process, on average, per day?

Locate the current world price of oil (US$/bbl) and the current retail price of regular gasoline in your area (per liter or per gallon, as appropriate). What is the markup in the price per unit energy between crude oil and retail gasoline?

Using the information in Figure 2.6 and the average composition of coal (lignite, sub-bituminous/bituminous and anthracite) in the United States, calculate the mass of the coal used annually. Use the average energy content for sub-bituminous/bituminous coal.

Estimate the total coal produced in the United Kingdom between 1820 and the present.

If shale oil replaced coal in the United States, how many years would the U.S. resources last at the current rate of use?

Locate the current world price of oil (US$/bbl), coal (bituminous coal, per tonne), and natural gas (per1000 m³). For each fossil fuel, calculate the cost of energy pergigajoule assuming that the fuel can be converted to usable energy with an efficiency of 100%.

For the reaction shown in equation (3.4), calculate the mass of CO and the mass of H₂ produced by the gasification of 1 kg of carbon. What is the energy content of these two products?