Calculate The Amount Of Energy That Would Come Out Of The GE
Calculate The Amount Of Energy That Would Come Out Of The Generator If
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 in a thermal power plant involves understanding the efficiencies of each component in the energy conversion chain. Given an input energy of 20,000,000 BTU into the boiler, and efficiencies for the boiler, turbine, and generator, we can determine the total energy output at the generator and the energy lost or transferred to the condenser.
Step 1: Calculate the energy input to the boiler.
The given energy input is 20,000,000 BTU. Since this is the input energy to the boiler, we proceed to determine how much useful energy is produced after the boiler's efficiency.
Step 2: Determine the energy produced by the boiler.
The boiler's efficiency is 81%, which means 81% of the input energy is converted into useful thermal energy.
\[
E_{\text{boiler output}} = E_{\text{input}} \times \eta_{\text{boiler}}
\]
\[
E_{\text{boiler output}} = 20,000,000 \times 0.81 = 16,200,000 \text{ BTU}
\]
Step 3: Calculate the energy extracted by the turbine.
The turbine converts thermal energy into mechanical energy with an efficiency of 43%.
\[
E_{\text{turbine output}} = E_{\text{boiler output}} \times \eta_{\text{turbine}}
\]
\[
E_{\text{turbine output}} = 16,200,000 \times 0.43 = 6,966,000 \text{ BTU}
\]
Step 4: Calculate the energy that reaches the generator.
The energy produced by the turbine is then converted into electrical energy by the generator with an efficiency of 98%.
\[
E_{\text{electricity}} = E_{\text{turbine output}} \times \eta_{\text{generator}}
\]
\[
E_{\text{electricity}} = 6,966,000 \times 0.98 = 6,826,680 \text{ BTU}
\]
Step 5: Determine the energy lost in the system and the energy transferred to the condenser.
The total initial energy input was 20,000,000 BTU. The energy that appears as useful work at the generator output is approximately 6,826,680 BTU. The remaining energy is primarily transferred to the condenser as waste heat or lost due to inefficiencies.
Calculating the energy dissipated, we consider:
\[
E_{\text{lost or transferred to condenser}} = E_{\text{input}} - E_{\text{electricity}}
\]
\[
E_{\text{lost or transferred to condenser}} = 20,000,000 - 6,826,680 = 13,173,320 \text{ BTU}
\]
This energy largely ends up in the condenser or as heat loss in the system.
Summary of Results:
- The energy output from the generator: 6,826,680 BTU
- The energy transferred to or lost in the condenser: 13,173,320 BTU
These calculations illustrate how the efficiencies of each component influence the overall energy conversion process in a thermal power plant.
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