An engine operates between 800 K and 400 K temperature, the inventor claims that its efficiency is 55%. Comment on his claim.
The inventor claims an engine's 55% efficiency operating between 800 K and 400 K. However, based on the Carnot efficiency formula, the actual efficiency is 50%.
SOLUTION : To evaluate the inventor's claim regarding the efficiency of the engine operating between temperatures of 800 K and 400 K, we can apply the principles of thermodynamics. The efficiency of a heat engine is determined by the temperature difference between the hot reservoir (800 K) and the cold reservoir (400 K).The efficiency of a heat engine is given by the Carnot Efficiency formula:
\[ \text{Efficiency} = 1 - \frac{T_c}{T_h} \]
where Efficiency is expressed as a decimal or percentage, and \(T_c\) and \(T_h\) represent the temperatures of the cold and hot reservoirs, respectively.
Substituting the given temperatures into the formula:
\[ \text{Efficiency} = 1 - \frac{400}{800} = 1 - 0.5 = 0.5 = 50\% \]
The calculated efficiency of the engine based on the Carnot efficiency formula is 50%, not 55% as claimed by the inventor. Therefore, the inventor's claim appears to be inaccurate.
It's important to note that the Carnot efficiency is an upper limit for the efficiency of any heat engine operating between the given temperature limits. Real-world engines may have lower efficiencies due to factors like friction, heat losses, and other inefficiencies.
In conclusion, based on the Carnot efficiency calculation, the inventor's claim of 55% efficiency for the engine operating between temperatures of 800 K and 400 K seems to be overstated. The actual efficiency calculated using the Carnot efficiency formula is 50%.
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