Maximum efficiency of a heat engine

In summary, the maximum efficiency of a heat engine is determined by the Carnot cycle and is given by the formula: maximum efficiency = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. This means that the efficiency can never be 100%, as some energy will always be lost to the environment. The second law of thermodynamics states that in any energy conversion, some energy will always be lost as heat to the environment. The maximum efficiency of a heat engine is limited by this law, as it is impossible to convert all of the energy into work without any losses. It is also impossible for the maximum efficiency to be greater than 1, as this
  • #1
JJones_86
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Homework Statement


Calculate the maximum possible efficiency of a heat engine that uses surface lake water at 19°C as a source of heat and rejects waste heat to the water 0.100 km below the surface where the temperature is 4.1°C.


Homework Equations


eta = 1 - Tc / Th


The Attempt at a Solution



eta = 1 - 277.1K/292K
eta = -.945548


Not sure what I'm doing wrong, am I not supposed to convert to Kelvin??
 
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  • #2
Nevermind, I've figured out what I did wrong, I was treating the equation like this (1-277.1K)/292K
 
  • #3


I would like to clarify that the maximum efficiency of a heat engine is determined by the Carnot cycle and is given by the equation eta = 1 - Tc / Th, where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. In this case, the hot reservoir is the surface lake water at 19°C, which is equivalent to 292K, and the cold reservoir is the water 0.100 km below the surface, which is at a temperature of 4.1°C or 277.1K. Therefore, the maximum efficiency of the heat engine can be calculated as follows:

eta = 1 - (277.1K/292K)
eta = 1 - 0.9476
eta = 0.0524 or 5.24%

This means that the maximum possible efficiency of the heat engine is 5.24%. It is important to note that this is the theoretical maximum efficiency and in practical applications, the efficiency may be lower due to various factors such as friction and heat losses.
 

1. What is the maximum efficiency of a heat engine?

The maximum efficiency of a heat engine is determined by the Carnot cycle and is given by the formula: maximum efficiency = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. This means that the efficiency can never be 100%, as some energy will always be lost to the environment.

2. How does the maximum efficiency of a heat engine relate to the second law of thermodynamics?

The second law of thermodynamics states that in any energy conversion, some energy will always be lost as heat to the environment. The maximum efficiency of a heat engine is limited by this law, as it is impossible to convert all of the energy into work without any losses.

3. Can the maximum efficiency of a heat engine be greater than 1?

No, the maximum efficiency of a heat engine can never be greater than 1. This would violate the first law of thermodynamics, which states that energy cannot be created or destroyed.

4. How can the maximum efficiency of a heat engine be improved?

The maximum efficiency of a heat engine can be improved by reducing the temperature difference between the hot and cold reservoirs, using a more efficient working fluid, and minimizing internal friction and heat losses within the engine.

5. Does the maximum efficiency of a heat engine depend on the type of fuel used?

No, the maximum efficiency of a heat engine is independent of the type of fuel used. It is solely determined by the temperatures of the hot and cold reservoirs and the Carnot efficiency formula. However, the type of fuel can affect the practical efficiency of the engine due to factors such as combustion efficiency and energy density.

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