Given data:
Refer to problem 13-17 accompanying table in the textbook, the average efficiency of the power plants is 35%.
The heating value of the coal is 7.5 MJkg.
Formula used:
Formula to calculate the power plant efficiency is,
Power plant effeicency=Energy generatedEnergy input from fuel
Rearrange the equation,
Energy input from fuel=Energy generatedpower plant effeicency (1)
Convert kWh to MJ,
1 kWh=3.6 MJ (2)
Formula to calculate the amount of coal required for generating one year is,
amount of coal required=Energy input from fuelHeating value of the coal (3)
Calculation:
Find the energy input from the fuel in each year:
Substitute 1161.562×109 kWh for energy generated and 0.35 (35%) for power plant efficiency in equation (1) to find energy input from the fuel in 1980.
Energy input from fuel=1161.562×109 kWh0.35=3.318748571×1012 kWhEnergy input from fuel≅3318.748571×109 kWh
Substitute 1594.011×109 kWh for energy generated and 0.35 (35%) for power plant efficiency in equation (1) to find energy input from the fuel in 1990.
Energy input from fuel=1594.011×109 kWh0.35=4.554317143×1012 kWhEnergy input from fuel≅4554.317143×109 kWh
Substitute 1966.265×109 kWh for energy generated and 0.35 for power plant efficiency in equation (1) to find energy input from the fuel in 2000.
Energy input from fuel=1966.265×109 kWh0.35=5.6179×1012 kWhEnergy input from fuel≅5617.9×109 kWh
Substitute 2040.913×109 kWh for energy generated and 0.35 for power plant efficiency in equation (1) to find energy input from the fuel in 2005.
Energy input from fuel=2040.913×109 kWh0.35=5.8318×1012 kWhEnergy input from fuel≅5831.18×109 kWh
Substitute 2217.555×109 kWh for energy generated and 0.35 for power plant efficiency in equation (1) to find energy input from the fuel in 2010.
Energy input from fuel=2217.555×109 kWh0.35=6.335871429×1012 kWhEnergy input from fuel≅6335.871429×109 kWh
Substitute 2504.786×109 kWh for energy generated and 0.35 for power plant efficiency in equation (1) to find energy input from the fuel in 2020.
Energy input from fuel=2504.786×109 kWh0.35=7.156531429×1012 kWhEnergy input from fuel≅7156.531429×109 kWh
Substitute 3380.674×109 kWh for energy generated and 0.35 for power plant efficiency in equation (1) to find energy input from the fuel in 2030.
Energy input from fuel=3380.674×109 kWh0.35=9.65906857×1012 kWhEnergy input from fuel≅9659.06857×109 kWh
Now convert all the values from kWh to MJ:
Substitute 3318.74857×109 kWh for 1 kWh in equation (2) for the year 1980,
3318.748571×109 kWh=(3.6 MJ)×(3318.748571×109) [∴1 kWh=3.6 MJ]=1.194749486×1013 MJ=11947.49486×109 MJ
Substitute 4554.317143×109 kWh for 1 kWh in equation (2) for the year 1990,
4554.317143×109 kWh=3.6 MJ×4554.317143×109 [∴1 kWh=3.6 MJ]=1.639554171×1013 MJ=16395.54171×109 MJ
Substitute 5617.9×109 kWh for 1 kWh in equation (2) for the year 2000,
5617.9×109 kWh=(3.6 MJ)(5617.9×109) [∴1 kWh=3.6 MJ]=2.022444×1013 MJ=20224.44×109 MJ
Substitute 5831.18×109 kWh for 1 kWh in equation (2) for the year 2005,
5831.18×109 kWh=(3.6 MJ)(5831.18×109) [∴1 kWh=3.6 MJ]=2.0992248×1013 MJ=20992.248×109 MJ
Substitute 6335.871429×109 kWh for 1 kWh in equation (2) for the year 2010,
6335.871429×109 kWh=(3.6 MJ)(6335.871429×109) [∴1 kWh=3.6 MJ]=2.280913714×1013 MJ=22809.13714×109 MJ
Substitute 7156.531429×109 kWh for 1 kWh in equation (2) for the year 2020,
7156.531429×109 kWh=(3.6 MJ)(7156.531429×109) [∴1 kWh=3.6 MJ]=2.576351314×1013 MJ=25763.51314×109 MJ
Substitute 9659.068571×109 kWh for 1 kWh in equation (2) for the year 2030,
Now find the amount of coal required in every year:
Substitute 11947.49486×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 1980,
amount of coal required=11947.49486×109 MJ7.5 MJkg=1.593×1012 kg≅1.59×1012 kg
Substitute 16395.54171×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 1990,
amount of coal required=16395.54171×109 MJ7.5 MJkg=2.18607×1012 kg≅2.19×1012 kg
Substitute 20224.44×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 2000,
amount of coal required=20224.44×109 MJ7.5 MJkg=2.696592×1012 kg≅2.7×1012 kg
Substitute 20992.248×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 2005,
amount of coal required=20992.248×109 MJ7.5 MJkg=2.79896×1012 kg≅2.8×1012 kg
Substitute 22809.13714×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 2010,
amount of coal required=22809.13714×109 MJ7.5 MJkg=3.04122×1012 kg≅3.04×1012 kg
Substitute 25763.51314×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 2020,
amount of coal required=25763.51314×109 MJ7.5 MJkg=3.43514×1012 kg≅3.44×1012 kg
Substitute 34772.64686×109 MJ for energy input from fuel and 7.5 MJkg for heating value of the coal in equation (3) to find amount of coal is required in 2030,
amount of coal required=34772.64686×109 MJ7.5 MJkg=4.63635×1012 kg≅4.64×1012 kg
Therefore, the energy input for all years for Coal, in kWh and MJ along with coal required to produce 35% of efficiency is shown in Table 1 (with approximately rounded values).
Table 1
Energy Produced (10^9 kWh) | Energy(considering efficiency) 109 kWh | Energy (considering efficiency) 109 MJ | Amount of coal needed in kg |
1161.562 | 3318.748571 | 11947.49486 | 1.59E+12 |
1594.011 | 4554.317143 | 16395.54171 | 2.19E+12 |
1966.265 | 5617.9 | 20224.44 | 2.70E+12 |
2040.913 | 5831.18 | 20992.248 | 2.80E+12 |
2217.555 | 6335.871429 | 22809.13714 | 3.04E+12 |
2504.786 | 7156.531429 | 25763.51314 | 3.44E+12 |
3380.674 | 9569.068571 | 34772.64686 | 4.64E+12 |
Conclusion:
Hence, the amount of coal (in kg) required for generating electricity for each year has been calculated.