Efficiency Assignment Submit Due Oct 31 By 11:59 PM Point

Efficiency Assignmentsubmit Assignmentdueoct 31by1159pmpoints20s

Calculate the amount of energy that would come out of the generator if 20,000,000 BTU went into the boiler. The boiler is 81% efficient, the turbine is 43% efficient, and the generator is 98% efficient. Also, calculate how much energy goes into the condenser. Save your answer to a Word document and upload to Canvas. It will help if you can show your steps by writing/typing out each step in detail.

Follow the steps in the presentation. If you write out the solution by hand instead of typing, you scan the paper and save it as a pdf. file and upload it as an attachment. Be sure the numbers in the data and the answers all have units. The decimal percents do not have units, of course.

Paper For Above instruction

The calculation of energy output from a thermal power plant involves a systematic step-by-step analysis of the energy conversions through each component of the system. Starting with the initial input energy into the boiler, we consider the efficiencies of all subsequent components—namely, the boiler, turbine, and generator—to determine the final electrical energy output. Additionally, we assess the energy lost or transferred into the condenser to understand the overall energy flow within the system.

Initially, we are given an input energy of 20,000,000 BTU into the boiler. Our goal is to determine the electric power generated and the amount of energy lost or transferred in the condenser.

Step 1: Calculate the usable heat after the boiler

The boiler efficiency is 81%, meaning 81% of the input energy is converted into thermal energy useful for the turbine. The thermal energy generated can be calculated as:

Q_thermal = Input energy × Boiler efficiency = 20,000,000 BTU × 0.81 = 16,200,000 BTU

Step 2: Energy conversion through the turbine

The turbine has an efficiency of 43%, representing how effectively it converts the thermal energy into mechanical energy, which then drives the generator. The mechanical energy output from the turbine is:

W_turbine = Q_thermal × Turbine efficiency = 16,200,000 BTU × 0.43 = 6,966,000 BTU

Step 3: Energy conversion through the generator

The generator's efficiency is 98%, indicating how much mechanical energy from the turbine is converted into electrical energy. The electrical energy output is:

W_electric = W_turbine × Generator efficiency = 6,966,000 BTU × 0.98 = 6,826,680 BTU

Step 4: Energy entering the condenser

The energy entering the condenser is essentially the thermal energy rejected after electricity generation, which can be calculated as:

Q_lost = Q_thermal - W_turbine = 16,200,000 BTU - 6,966,000 BTU = 9,234,000 BTU

This energy is primarily dissipated as heat in the condenser to maintain the cycle and ensure efficient operation.

Summary of Results

• Electrical energy produced: 6,826,680 BTU
• Energy into the condenser: 9,234,000 BTU

Conclusion

The systematic analysis illustrates that out of the initial 20 million BTU input, approximately 6.83 million BTU is converted into electrical energy, while about 9.23 million BTU is expelled into the condenser. These calculations demonstrate the importance of component efficiencies in determining the overall performance of a thermal power generation system. Improving efficiencies at each stage could significantly enhance the net electrical output and system sustainability. This detailed step-by-step approach not only verifies the theoretical energy conversions but also highlights the energy losses inherent to practical energy conversion processes.

References

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