As I understand: ## \eta ## is not defined during a process. ## \eta ## is defined for a process. For a Carnot engine working between temperatures ## T_h ## and ## T_f ##, ## \eta ## is defined as ## \frac W{Q_h} ##. This is what I have used.TSny said:
The temperatures of the two reservoirs are changing during the process. So you can't use the results for a single Carnot cycle with constant reservoir temperatures. You can't get from the initial state of this system to the final state reversibly with a single Carnot cycle. You need to use multiple Carnot cycles, each with slightly different pair of reservoir temperatures. And, for each of these multiple Carnot cycles, the efficiency is different.Pushoam said:
I didn't realize that the temperatures of the reservoirs are changing and the efficiency eqn is valid for constant reservoir temperatures even after solving the question.Chestermiller said:
A Carnot engine is an idealized heat engine that operates on the Carnot cycle, which is a theoretical thermodynamic cycle involving two isothermal processes and two adiabatic processes. It is often used as a benchmark for comparing the efficiency of real-world heat engines.
A Carnot engine works by absorbing heat from a high-temperature reservoir, performing work, and then releasing excess heat to a low-temperature reservoir. This process is repeated in a continuous cycle, with the engine's efficiency depending on the temperature difference between the two reservoirs.
The maximum work done by a Carnot engine is equal to the difference in temperature between the two reservoirs, divided by the temperature of the high-temperature reservoir. This is known as the Carnot efficiency and is represented by the formula W(max) = (Th - Tl) / Th, where Th is the temperature of the high-temperature reservoir and Tl is the temperature of the low-temperature reservoir.
The maximum work done by a Carnot engine is important because it represents the theoretical upper limit for the efficiency of any heat engine. This means that no real-world heat engine can ever be more efficient than a Carnot engine operating between the same temperature reservoirs. It also allows for the comparison and evaluation of the efficiency of different heat engines.
The maximum work done by a Carnot engine can only be increased by increasing the temperature difference between the two reservoirs. This can be achieved by using a higher temperature heat source or a lower temperature heat sink. However, in reality, it is difficult to achieve large temperature differences and therefore, the Carnot efficiency remains a theoretical limit for the efficiency of heat engines.
