B. A coal fired power plant has a condenser that extracts 17,500 BTU/kg of burne
ID: 3348880 • Letter: B
Question
B. A coal fired power plant has a condenser that extracts 17,500 BTU/kg of burned coal. Compute the mechanical energy of the turbine and the overall system efficiency. Repeat for natural gas and oil fired plant. Compare the efficiency of the plant in three cases. The thermal energy constant (TEC) for the fossil fuels are: Fuel Type Coal Natural Gas Oil TEC (BTU/kg) 27,000 48,000 45,000 C. Estimate the amount of nuclear energy produced by a 15 kg mass of Uranium-235. It is given that each fission event releases approximately 3.2 x 1011 J of energy. One kg of 235U can have approximately 25.4x 1023 fission eventsExplanation / Answer
B.
The mechanical energy of the turbine is given as the difference between source energy and the energy dissipated in the condensor.
Thermal energy constant (TEC)is the thermal energy produced per kg of fuel.
TEC for coal = 27000 BTU/kg. This is the source energy. Let it be Q1.
It is given that the condensor extracts 17500 BTU/kg. This is the energy dissipated at the condensor. Let it be denoted by Q2.
Hence, Mechanical energy of the turbine = 27000 - 17500 = 9500 BTU/kg = 9500*1055 joules/kg = 10022.5 kJ/kg (Taking 1BTU = 1055 joules)
Efficiency of the system = output / input.
Output is the mechanical energy of the turbine and input is the source energy Q1.
Efficiency = (9500/17500) * 100 = 35.18 %.
For natural gas and oil fired plant, take Q1 as respective TEC and Q2 as 17500 BTU/kg.
Natural Gas
Here source energy Q1 = 48000BTU/kg.
Mechanical Energy of the turbine = 48000 - 17500 = 30500 BTU/kg = 32177.5 kJ/kg.
Efficiency = (30500/48000) *100 = 63.54%.
Oil
Mechanical Energy of turbine = 45000 - 17500 = 27500 BTU/kg = 29012.5 kJ/kg.
Efficiency = (27500/45000) * 100 = 61.11%.
Comparison of efficiency in percentage
It is seen that the efficiency of Natural Gas Plant is the highest of the three and that of coal plant is the lowest. Also, it is seen that as TEC increases, efficiency is improved given that energy extracted by the condensor remains same.
------------------------------------------------------------------------------------------------------------------------------------
C.
Given that 1 fission releases 3.2 * 10-11 J energy and one kg of Uranium - 235 has 25.4 * 1023 fission events.
Therefore
energy produced by 1 kg Uranium 235 = energy released by 1 fission event * number of fission events
= (3.2 * 10 -11 ) * (25.4 * 10 23) = 8.128 * 1013 J
Amount of nuclear energy produced by 15 kg Uranium = 8.128 * 1013 * 15 = 1.219 * 1015 J
------------------------------------------------------------------------------------------------------------------------------
Coal 35.18 Natural Gas 63.54 Oil 61.1Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.