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The National Grid is supplied mainly from power stations which have overall efficiencies of up to about 40% Table 1 shows the average power requirements of a large paper-manufacturing business (a paper mill) - AQA - A-Level Physics - Question 4 - 2018 - Paper 6
Question 4
The National Grid is supplied mainly from power stations which have overall efficiencies of up to about 40% Table 1 shows the average power requirements of a large ... show full transcript
Worked Solution & Example Answer:The National Grid is supplied mainly from power stations which have overall efficiencies of up to about 40% Table 1 shows the average power requirements of a large paper-manufacturing business (a paper mill) - AQA - A-Level Physics - Question 4 - 2018 - Paper 6
Step 1
explain why the maximum theoretical efficiency of a heat engine is much less than 100%
Answer
The maximum theoretical efficiency of a heat engine is derived from the second law of thermodynamics, which states that no engine can be 100% efficient due to irreversible processes and heat losses that occur during operation. Factors such as friction, incomplete combustion, and energy dissipation through heat contribute to the inefficiencies in the system.
For a heat engine operating between two temperature reservoirs, the maximum efficiency can be calculated using:
Where ( T_{hot} ) is the absolute temperature of the heat source and ( T_{cold} ) is the absolute temperature of the heat sink. Since achieving maximum thermodynamic efficiency requires perfect conditions and no losses, real systems always perform below this theoretical maximum.
Step 2
use the information above, including the numerical data, to come up with a reasoned conclusion
Answer
Given that the paper mill has a total power requirement of:
- Motors: 49 MW
- Heating: 141 MW
- Electrical equipment: 8 MW
Total = 49 + 141 + 8 = 198 MW required.
If the paper mill decides to use the National Grid entirely, it may face issues related to supply fluctuations and high costs. On the other hand, if they opt for a 60 MW gas turbine CHP scheme with 36% efficiency, the output power available would be:
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Electrical output: ( 60 \text{ MW} \times 0.36 = 21.6 \text{ MW} )
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The thermal energy available for heating would be calculated from the remaining energy:
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Total input energy is:
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Deducting the electrical output:
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Thermal energy = 166.67 MW - 21.6 MW = 145.07 MW (approximately).
This shows that using CHP could satisfy the heating requirement but would still leave the paper mill short on total energy needs, thus a supplementary supply from the National Grid may still be required. Additionally, the installation cost and maintenance considerations of a CHP system would also need to be evaluated relative to its potential energy savings.