An inventor says that his new concept of an engine, while working betw...
The efficiency of any reversible engine cannot be more than that of Carnot cycle. For the given case, the Carnot cycle efficiency is
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An inventor says that his new concept of an engine, while working betw...
The inventor claims that his new engine concept operates between temperature limits of 27°C and 327°C and rejects 45% of the heat absorbed from the source. We need to determine which engine this concept is equivalent to.
To solve this problem, we can use the concept of efficiency and compare it to the efficiencies of different types of engines.
Efficiency of an engine is defined as the ratio of useful work output to the heat input. It can also be expressed as 1 minus the ratio of rejected heat to the heat input.
Let's analyze each of the given options to see which one matches the conditions provided by the inventor:
a) Carnot engine:
The Carnot engine is the most efficient engine that operates between two temperature limits. Its efficiency is given by the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the absolute temperature of the cold reservoir and Th is the absolute temperature of the hot reservoir. In this case, the temperature limits provided by the inventor are 27°C and 327°C.
Calculating the efficiency for the Carnot engine using these temperature limits:
Efficiency = 1 - (27 + 273)/(327 + 273) = 1 - 300/600 = 0.5
The efficiency of the Carnot engine is 0.5, which does not match the 45% rejection of heat claimed by the inventor. Therefore, option a) is not the correct answer.
b) Diesel engine:
The efficiency of a Diesel engine is typically lower than that of a Carnot engine. Therefore, it is unlikely that the inventor's concept would be equivalent to a Diesel engine. Option b) is not the correct answer.
c) Impossible engine:
This option suggests that the inventor's concept is not physically possible, meaning it violates the laws of thermodynamics. Without further information, it is difficult to determine if this is the correct answer. However, based on the given information, it is not clear why the inventor's concept would be considered impossible. Therefore, it is unlikely that this is the correct answer.
d) Ericsson engine:
The Ericsson engine is a heat engine that operates on a thermodynamic cycle similar to the Carnot cycle but with a constant pressure heat addition and rejection process. It is known for its high efficiency. However, without specific information about the efficiency of the Ericsson engine, it is difficult to determine if this is the correct answer.
Based on the given information, it is most likely that the inventor's concept is not equivalent to any of the listed engines. Therefore, option c) is the correct answer.
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