lzh said:Homework Statement
The exhaust temperature of a Carnot heat engine is 121◦C. What is the intake temperature if the efficiency of the engine is 13.4 %? Answer in units of ◦C.
Homework Equations
e=1-(Tc/Th)
The Attempt at a Solution
This seems like just a plug and chug problem:
0.134=1-(121/Th)
Th=139.723 ◦C
However, this answer is wrong-according to my Quest web homework. Am I missing something here? Thanks
A Carnot engine is a theoretical heat engine that operates on the Carnot cycle, which consists of two isothermal (constant temperature) and two adiabatic (no heat exchange) processes. It works by converting heat energy into mechanical work through a series of steps involving expansion, compression, and heat exchange with a hot and cold reservoir.
The efficiency of a Carnot engine is given by the formula: efficiency = 1 - (Tcold/Thot), where Tcold is the temperature of the cold reservoir and Thot is the temperature of the hot reservoir. This means that the efficiency of a Carnot engine is dependent on the temperature difference between the two reservoirs.
The Carnot engine is considered to be the most efficient heat engine because it operates on a theoretical cycle that has the highest possible efficiency for a given temperature difference between the hot and cold reservoir. This is known as the Carnot efficiency and is a result of the reversible nature of the Carnot cycle.
The exhaust problem in a Carnot engine refers to the fact that in order to achieve the maximum theoretical efficiency, the temperature of the exhaust gas must be equal to the temperature of the cold reservoir. This means that all of the heat energy from the hot reservoir has been converted into mechanical work, leaving no excess heat to be expelled from the engine. However, in reality, some heat is always lost in the exhaust, resulting in a lower efficiency.
The exhaust problem can be minimized by increasing the temperature difference between the hot and cold reservoirs. This results in a higher Carnot efficiency and a smaller temperature difference between the exhaust gas and the cold reservoir, reducing heat loss in the exhaust. Additionally, using more efficient heat exchange methods and insulating the engine can also help reduce the exhaust problem.