You have to show us what you have done to solve the problem. Please follow the homework template.junfan02 said:A Carnot engine is operating between a source and a sink at temperatures T1 & T2 (T1>T2) respectively..
The heat capacities of the source and the sink are equal.
Find the final temperature attained.
junfan02 said:dQ amount of heat taken away from the aource reduces its temperature by dQ/c.
Assuming c to be the common heat capacity. And the increase in temperature of the sink for this cycle is T2*dQ/(T1*c)
How do I proceed after this?
So work out the expression for the change in entropy of each reservoir and set their sum equal to 0!junfan02 said:The total change in entropy obviously has to be zero since this is a reversible process!
A Carnot engine is an idealized heat engine that operates on the Carnot cycle, which is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It was originally conceptualized by French physicist Nicolas Léonard Sadi Carnot in the 19th century.
A Carnot engine works by taking in heat energy from a high-temperature reservoir, converting some of that energy into work, and then releasing the remaining heat energy to a low-temperature reservoir. This process is repeated in a continuous cycle, with the engine operating at maximum efficiency when it follows the Carnot cycle.
The final temperature attained by a Carnot engine depends on the temperatures of the high- and low-temperature reservoirs, as well as the efficiency of the engine. The final temperature can be calculated using the Carnot efficiency formula: T2 = T1(1 - 1/η), where T1 is the temperature of the high-temperature reservoir, T2 is the temperature of the low-temperature reservoir, and η is the efficiency of the engine.
The efficiency of a Carnot engine can be calculated using the Carnot efficiency formula: η = (T1 - T2)/T1, where T1 is the temperature of the high-temperature reservoir and T2 is the temperature of the low-temperature reservoir. This formula shows that the efficiency of a Carnot engine increases as the temperature difference between the two reservoirs increases.
The Carnot engine is a theoretical concept and does not exist in its idealized form in the real world. However, the principles of the Carnot cycle have been applied in the design of certain heat engines, such as steam engines and gas turbines. It is also used as a benchmark for comparing the efficiency of other engines and for understanding the limitations of real-world thermodynamic processes.