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Explain how the second law of thermodynamics predicts that a heat engine can never be 100% efficient - AQA - A-Level Physics - Question 5 - 2020 - Paper 5
Question 5
Explain how the second law of thermodynamics predicts that a heat engine can never be 100% efficient. This is because the second law of thermodynamics states that h... show full transcript
Worked Solution & Example Answer:Explain how the second law of thermodynamics predicts that a heat engine can never be 100% efficient - AQA - A-Level Physics - Question 5 - 2020 - Paper 5
Step 1
Explain how the second law of thermodynamics predicts that a heat engine can never be 100% efficient.
Answer
The second law of thermodynamics asserts that a heat engine requires a hot and a cold reservoir to operate effectively. It states that not all heat absorbed can be converted into work; some must be expelled to the cold reservoir. Thus, the efficiency, defined as the ratio of work output to heat input, cannot reach 100%. In hypothetical terms, achieving 100% efficiency would mean no heat loss to a cold reservoir, which is unachievable as it would necessitate operating at absolute zero, forbidden by the laws of physics.
Step 2
A company plans to build a geothermal power station in a region where there is hot rock deep below the surface. The scheme is shown in Figure 7.
Answer
In a geothermal power station where the electrical power output is 2.9 MW, the provided claim of generating 6.4 MW from the power station requires examination through the lens of thermodynamic principles. Based on Carnot efficiency, maximum efficiency for a heat engine operating between temperatures would be calculated as:
Here, the absolute temperatures must be used. At 175°C (which is 448 K) and a cold sink of 30°C (which is 303 K), we have:
Applying this efficiency to the energy input:
- The power output cannot exceed this 32% without violating thermodynamic principles. Thus, the maximum output power can be given as:
Given that the input power required (from the company's claims) corresponds to a maximum of 9.1 MW, which indicates:
Any claim suggesting more than 2.91 MW from an input of 2.9 MW contradicts the second law of thermodynamics. Thus, the company's assertion of 6.4 MW generation is not feasible.