Question

How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot cycle operating between the same temperature limits?

Short answer

Answer: The thermal efficiency of an ideal cycle is generally less than or equal to the thermal efficiency of a Carnot cycle when given the same temperature limits. The Carnot cycle is the most efficient reversible cycle and is used as a benchmark to compare other cycles.

Step-by-step solution

Define the thermal efficiency formula

The thermal efficiency of any cycle is given by the formula: Efficiency (η) = (Work output) / (Heat input)

Define the efficiency of an ideal cycle

The efficiency of an ideal cycle depends on the specific processes within the cycle. There are different ideal cycles, such as the Otto cycle, Diesel cycle, and Brayton cycle, each with its thermal efficiency formula. In general, the thermal efficiency for an ideal cycle can be written as: η_ideal = f(T1, T2) Where T1 and T2 are the temperature limits of the cycle, and f(T1, T2) is a function that varies between different ideal cycles.

Define the efficiency of a Carnot cycle

The efficiency of a Carnot cycle operating between two temperature limits T1 (hot/reservoir source) and T2 (cold/reservoir sink) is given by: η_carnot = 1 - T2/T1

Compare the thermal efficiency of an ideal cycle and a Carnot cycle

As mentioned earlier, the Carnot cycle is the most efficient reversible cycle, which means its efficiency is always higher than or equal to any other cycle, including ideal cycles, operating between the same temperature limits. So, the general comparison between the thermal efficiency of an ideal cycle and a Carnot cycle is: η_ideal ≤ η_carnot This means that the thermal efficiency of an ideal cycle is less than or equal to the thermal efficiency of a Carnot cycle.