Quick Question- carnot efficiency

In summary, when calculating the maximum possible efficiency of an engine using multiple heat reservoirs, it is not valid to simply take the average of the temperatures of the hot reservoirs and the average of the temperatures of the heat sinks. The calculation should be a weighted average, taking into account the flow rates and heat capacities of each reservoir. This is important because using a simple average could result in an unrealistically high efficiency, as demonstrated by the example of a 99% flow from a 400K reservoir and 1% flow from a 1000K reservoir.
  • #1
trelek2
88
0
Suppose an engine uses multiple heat reservoirs:

When calculating the carnot (maximum possible efficiency) is it valid to simply take the average of the temperatures of the hot reservoirs from which the heat is extracted as T(hot) and the average of the temperatures of the heat sinks to which heat is rejected as T(cold)??
(regardless of the amounts of energy Q rejected/extracted from each of the reservoirs)
 
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  • #2
I think you'd have to do a weighted average, based on flow rates and heat capacities or how they mix.

Put it this way if you have 99% flow from 400K reservoir and 1% from 1000K
using a average temp of 700K would give an unrealistically high efficieny.

This is all assuming I've undersood your original question correctly.
 
  • #3
I agree with xxChrisxx; it all depends on how much heat is being removed from each reservoir per cycle.
 

Related to Quick Question- carnot efficiency

1. What is Carnot efficiency and how is it calculated?

Carnot efficiency is a measure of how efficiently a heat engine can convert heat energy into work. It is calculated by dividing the difference between the hot and cold temperatures by the hot temperature, and then subtracting the result from 1.

2. What is the significance of Carnot efficiency in thermodynamics?

Carnot efficiency is significant because it represents the theoretical maximum efficiency that any heat engine can achieve. It serves as a benchmark for evaluating the performance of real-world heat engines.

3. What factors can affect the Carnot efficiency of a heat engine?

The Carnot efficiency of a heat engine can be affected by the temperature of the hot and cold reservoirs, the nature of the working fluid, and any energy losses due to friction or other inefficiencies in the engine.

4. Can the Carnot efficiency of a heat engine ever be achieved in practice?

No, the Carnot efficiency is a theoretical limit and cannot be achieved in practice. Real-world heat engines are subject to energy losses and other inefficiencies that prevent them from reaching the maximum efficiency.

5. How does the concept of Carnot efficiency relate to the second law of thermodynamics?

The concept of Carnot efficiency is closely related to the second law of thermodynamics, which states that heat cannot spontaneously flow from a colder body to a hotter body. The Carnot efficiency represents the maximum efficiency that can be achieved in any heat engine, and it is a direct consequence of the second law.

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