Intake Temperature for a 40.2% Efficient Carnot Engine

In summary, a Carnot engine is a theoretical engine that converts heat energy into mechanical work by using a reversible cycle of four processes. The Carnot efficiency, which is the maximum possible efficiency of a heat engine, is calculated by dividing the temperature difference between two reservoirs by the temperature of the hot reservoir. However, there are limitations to a Carnot engine as it cannot be built in reality and does not account for factors such as friction and heat loss. It also cannot operate at 100% efficiency due to the second law of thermodynamics. The Carnot cycle is different from other thermodynamic cycles in that it is a theoretical concept and operates between two fixed temperatures. Other cycles, such as the Otto and Diesel cycles, are used in
  • #1
shar_p
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Homework Statement


The exhaust temperature of a Carnot heat engine is 401◦ C.
What is the intake temperature if the efficiency of the engine is 40.2 %?
Answer in units of ◦ C.


Homework Equations



e = 1 - Tc/Th (all in Kelvin)


The Attempt at a Solution


0.402 = 1 - Tc/ (401+273) = 1 - Tc/674
Tc = 0.598 * 674 = 403.052
Tc in C = 403.052-273 = 130.052

But somehow this answer seems to be wrong on the quest. This is my last problem ..please help? What am I doing wrong? Am I missing something?
 
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  • #2
You were given Tc to get Th, not the other way around like you did.
 
  • #3
Thanks .. that worked.
 

Related to Intake Temperature for a 40.2% Efficient Carnot Engine

1. What is a Carnot engine and how does it work?

A Carnot engine is a theoretical engine that operates between two heat reservoirs and converts heat energy into mechanical work. It works by using a reversible cycle of four processes (isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression) to transfer heat from a hot reservoir to a cold reservoir and produce work.

2. What is the Carnot efficiency and how is it calculated?

The Carnot efficiency is the maximum possible efficiency of a heat engine operating between two temperatures. It is calculated by dividing the temperature difference between the two reservoirs by the temperature of the hot reservoir (1 - Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

3. What are the limitations of a Carnot engine?

The Carnot engine is a theoretical concept and cannot be built in reality. It assumes that all processes are reversible, which is not possible in the real world. Additionally, it does not take into account factors such as friction and heat loss, which would decrease its efficiency.

4. Can a Carnot engine operate at 100% efficiency?

No, a Carnot engine cannot operate at 100% efficiency. It can only reach an efficiency of 1 - Tc/Th, which is less than 100% for any temperature difference between the two reservoirs. This is due to the second law of thermodynamics, which states that it is impossible to convert all heat energy into work without any loss.

5. How is the Carnot cycle different from other thermodynamic cycles?

The Carnot cycle is different from other thermodynamic cycles in that it is a theoretical concept and cannot be achieved in practice. Other thermodynamic cycles, such as the Otto and Diesel cycles, are used in real engines and take into account factors such as friction and heat loss. The Carnot cycle also operates between two fixed temperatures, while other cycles may have varying temperatures throughout the cycle.

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