Maximum efficiency = Carnot cycle

In summary, the maximum efficiency for a heat engine can be represented by the equation \eta = 1 - \frac{T_c}{T_h}, where T_c is the temperature of the cold sink and T_h is the temperature of the warm sink. This means that a Carnot cycle is the most efficient engine. However, it is not accurate to say that the efficiency of a Carnot cycle is 100%. This can be proven through various resources such as undergraduate textbooks on heat and thermodynamics or online sources like the one provided.
  • #1
LTP
24
0
Is it possible to show that the maximum efficiency for a heat engine is given by
[tex]\eta = 1 - \frac{T_c}{T_h}[/tex]
where [tex]T_c[/tex] is the temperature of the cold sink and [tex]T_c[/tex] is the temperature of the warm sink?

In other words: How do I prove that a engine run by a Carnot cycle is the most efficient engine?
 
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  • #3
can we take the efficiency of carnot cycle as 100%
or
can we say that the efficiency of carnot cycle is 100%?
 
  • #4
No, we most certainly can't.
 

1. What is the Carnot cycle and how does it relate to maximum efficiency?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The maximum efficiency of any heat engine is given by the Carnot efficiency, which is equal to the ratio of the temperature difference between the hot and cold reservoirs to the temperature of the hot reservoir.

2. Why is the Carnot cycle considered the most efficient cycle?

The Carnot cycle is considered the most efficient cycle because it is reversible and operates between two fixed temperature reservoirs. This means that all of the heat energy is converted into work without any losses due to friction or other inefficiencies. This is not possible with any real-world heat engine, but it serves as an ideal benchmark for maximum efficiency.

3. Is the Carnot efficiency achievable in real-world systems?

No, the Carnot efficiency is a theoretical limit and is not achievable in real-world systems. This is because all real-world systems involve some form of irreversibility, such as friction, which leads to energy losses and decreases the overall efficiency. However, engineers strive to design systems that approach the Carnot efficiency as closely as possible.

4. What is the formula for calculating the Carnot efficiency?

The Carnot efficiency is calculated using the equation: 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 increases as the temperature difference between the two reservoirs increases.

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

The Carnot cycle is based on the second law of thermodynamics, which states that heat cannot spontaneously flow from a colder object to a hotter object. The Carnot cycle follows this principle by only allowing heat to flow from the hot reservoir to the cold reservoir, and by minimizing any energy losses during the cycle. This makes it an ideal example of a reversible process, which is a key concept in the second law of thermodynamics.

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