Solutions Manual for
Introduction to Renewable Energy Conversions 2nd Edition
Sergio C. Capareda
CRC Press, Taylor and Francis Group
Boca Raton, Florida, USA
September 2025
0
,1
, Chapter 1
Introduction to Renewable Energy
1.7 Solved Problems
Problem 1.7.1 Carbon Dioxide Required to Make Carbohydrates
Problem 1.7.1 Determine the amount of carbohydrate or glucose produced (in tonnes) for every
tonne of carbon dioxide used by way of Equation 1.2.
Solution:
a. Equation 1.2 may be converted into units of weight using the molecular weights of the
compounds involved. The molecular weights of carbon is 12 g/mole and that for
hydrogen is 1 g/mol and oxygen is 16 g/mol.
b. 6𝐶𝐶𝑂𝑂2 + 6𝐻𝐻2 𝑂𝑂 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 → 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 + 6𝑂𝑂2
c. Thus, the amount of glucose (C6H12O6) produced per tonne of CO2 consumed is
calculated as follows:
𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 1 × [(6 × 12) + (12 × 1) + (6 × 16)] 180 𝑔𝑔 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6
=� �= = 0.75
6𝐶𝐶𝑂𝑂2 6 × �12 + 2 × (16)� 364 𝑔𝑔 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐶𝐶𝑂𝑂2
d. Theoretically, it would require about one-and-a-half tonnes of CO2 to generate a tonne of
carbohydrate (glucose) sugar.
Problem 1.7.2. Kinetic Energy of a Mass of Wind
Problem 1.7.2 Determine the kinetic energy available from a 100 kg of air moving at a speed of
12 m/s. Report the answer in units of Joules and in Btu.
Solution
a. Using Equation 1.1, the given values are simply plugged in the equation as follows:
1 12 𝑚𝑚 2 𝑁𝑁×𝑠𝑠 2
b. 𝐾𝐾𝐾𝐾 = × 100 𝑘𝑘𝑘𝑘 × � � × 𝑘𝑘𝑘𝑘×𝑚𝑚 = 7,200 𝑁𝑁 − 𝑚𝑚 = 7.2 𝑘𝑘𝑘𝑘
2 𝑠𝑠
2
, c. Thus, the equivalent unit in English system is shown below.
𝐵𝐵𝐵𝐵𝐵𝐵
𝐾𝐾𝐾𝐾 = 7,200 𝐽𝐽 × = 6.82 𝐵𝐵𝐵𝐵𝐵𝐵
1055 𝐽𝐽
d. Note the difference in the order of magnitude of Joules and Btu. One should always
remember the conversion of Joules to Btu using the relationship 1055 Joules/Btu.
Problem 1.7.3 Carbon Dioxide Production During Ethanol Fermentation
Problem 1.7.3 Determine the amount of carbon dioxide produced (kgs) for every kg of glucose
(𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 ) consumed in its conversion into ethanol. Use Equation 1.4 shown below in your
calculations. Convert these units into English units of lbs CO2 per lb glucose.
𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 + 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 → 2𝐶𝐶2 𝐻𝐻5 𝑂𝑂𝑂𝑂 + 2𝐶𝐶𝑂𝑂2 + ℎ𝑒𝑒𝑒𝑒𝑒𝑒
Solution:
a. The amount of carbon dioxide produced per weight of glucose is given as follows:
𝑘𝑘𝑘𝑘 𝐶𝐶𝐶𝐶2 2𝐶𝐶𝑂𝑂2 2 × [(1 × 12) + (2 × 16)] 88 𝑔𝑔
= =� �=
𝑘𝑘𝑘𝑘 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 [(6 × 12) + (12 × 1) + (6 × 16)] 180 𝑔𝑔
𝑘𝑘𝑘𝑘 𝐶𝐶𝑂𝑂2
= 0.49
𝑘𝑘𝑘𝑘 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6
b. The amount of CO2 produced per lb of glucose consumed should also be equal to 0.49
kg/kg or lb/lb.
Problem 1.7.4. Theoretical and Actual Power from Water Stream
Problem 1.7.4 Determine the theoretical and actual power that can be derived from a water
stream with a volumetric flow rate of 55 L/s and with a dynamic head of 2.0 m. Assume an
overall conversion efficiency of 45%.
Solution:
3
Introduction to Renewable Energy Conversions 2nd Edition
Sergio C. Capareda
CRC Press, Taylor and Francis Group
Boca Raton, Florida, USA
September 2025
0
,1
, Chapter 1
Introduction to Renewable Energy
1.7 Solved Problems
Problem 1.7.1 Carbon Dioxide Required to Make Carbohydrates
Problem 1.7.1 Determine the amount of carbohydrate or glucose produced (in tonnes) for every
tonne of carbon dioxide used by way of Equation 1.2.
Solution:
a. Equation 1.2 may be converted into units of weight using the molecular weights of the
compounds involved. The molecular weights of carbon is 12 g/mole and that for
hydrogen is 1 g/mol and oxygen is 16 g/mol.
b. 6𝐶𝐶𝑂𝑂2 + 6𝐻𝐻2 𝑂𝑂 + 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 → 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 + 6𝑂𝑂2
c. Thus, the amount of glucose (C6H12O6) produced per tonne of CO2 consumed is
calculated as follows:
𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 1 × [(6 × 12) + (12 × 1) + (6 × 16)] 180 𝑔𝑔 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6
=� �= = 0.75
6𝐶𝐶𝑂𝑂2 6 × �12 + 2 × (16)� 364 𝑔𝑔 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐶𝐶𝑂𝑂2
d. Theoretically, it would require about one-and-a-half tonnes of CO2 to generate a tonne of
carbohydrate (glucose) sugar.
Problem 1.7.2. Kinetic Energy of a Mass of Wind
Problem 1.7.2 Determine the kinetic energy available from a 100 kg of air moving at a speed of
12 m/s. Report the answer in units of Joules and in Btu.
Solution
a. Using Equation 1.1, the given values are simply plugged in the equation as follows:
1 12 𝑚𝑚 2 𝑁𝑁×𝑠𝑠 2
b. 𝐾𝐾𝐾𝐾 = × 100 𝑘𝑘𝑘𝑘 × � � × 𝑘𝑘𝑘𝑘×𝑚𝑚 = 7,200 𝑁𝑁 − 𝑚𝑚 = 7.2 𝑘𝑘𝑘𝑘
2 𝑠𝑠
2
, c. Thus, the equivalent unit in English system is shown below.
𝐵𝐵𝐵𝐵𝐵𝐵
𝐾𝐾𝐾𝐾 = 7,200 𝐽𝐽 × = 6.82 𝐵𝐵𝐵𝐵𝐵𝐵
1055 𝐽𝐽
d. Note the difference in the order of magnitude of Joules and Btu. One should always
remember the conversion of Joules to Btu using the relationship 1055 Joules/Btu.
Problem 1.7.3 Carbon Dioxide Production During Ethanol Fermentation
Problem 1.7.3 Determine the amount of carbon dioxide produced (kgs) for every kg of glucose
(𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 ) consumed in its conversion into ethanol. Use Equation 1.4 shown below in your
calculations. Convert these units into English units of lbs CO2 per lb glucose.
𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 + 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 → 2𝐶𝐶2 𝐻𝐻5 𝑂𝑂𝑂𝑂 + 2𝐶𝐶𝑂𝑂2 + ℎ𝑒𝑒𝑒𝑒𝑒𝑒
Solution:
a. The amount of carbon dioxide produced per weight of glucose is given as follows:
𝑘𝑘𝑘𝑘 𝐶𝐶𝐶𝐶2 2𝐶𝐶𝑂𝑂2 2 × [(1 × 12) + (2 × 16)] 88 𝑔𝑔
= =� �=
𝑘𝑘𝑘𝑘 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6 [(6 × 12) + (12 × 1) + (6 × 16)] 180 𝑔𝑔
𝑘𝑘𝑘𝑘 𝐶𝐶𝑂𝑂2
= 0.49
𝑘𝑘𝑘𝑘 𝐶𝐶6 𝐻𝐻12 𝑂𝑂6
b. The amount of CO2 produced per lb of glucose consumed should also be equal to 0.49
kg/kg or lb/lb.
Problem 1.7.4. Theoretical and Actual Power from Water Stream
Problem 1.7.4 Determine the theoretical and actual power that can be derived from a water
stream with a volumetric flow rate of 55 L/s and with a dynamic head of 2.0 m. Assume an
overall conversion efficiency of 45%.
Solution:
3
