Carnot engine acting upon another Carnot engine

In summary, the conversation discusses the efficiency of a black box acting as an engine when delivering power to a load. The efficiency is determined by the ratio of the power delivered to the load (P_{\ell}) and the power applied to the black box (P_b). The conversation also introduces the concept of an additional device (in series) applying an emf and current, which can affect the efficiency of the black box. The equation for energy conservation is given for both the "non-assisted" and "assisted" cases. The question asks about the efficiency of the black box when the additional device is "assisting" the applied emf and increasing the power delivered to the load. The attempt at a solution uses a guessed
  • #1
bjnartowt
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Homework Statement


Suppose an amount of power P_{\ell} is delivered to a load by a black box with potential difference V_T across it, driving current I through a single loop. If an amount of power P_b is applied to the black box, to sustain I at V_T, then the efficiency of this black box acting as an engine is P_{\ell}/P_b.

Now, suppose you have exactly the same black box, exactly the same load, but an additional device (in series, so it's still a single loop) applying an emf E_{ap} and a current I. The black box may still supply power, but if E_{ap} is large enough in magnitude, the black box becomes a load. However, the black box dissipates less power when the amount of power P_b applied earlier is applied to the black box. More power P_{\ell} is delivered to the load due to the application of P_b.

My question is: what would be the efficiency of the black box (if such a quantity exists) in its increasing P_{\ell} due to the application of P_b when it is "assisting" the applied emf E_{ap}?

Homework Equations


Energy conservation is P_{\ell} = V_T * I in the "non-assisted" case, and P_{\ell} = (E_{ap} - V_T) * I in the "assisted" case.

The Attempt at a Solution


I tried "guessing" an efficiency of P_{\ell} / (P_b + I * E_{ap}). If P_b is the heat flow from a temperature-difference between temperatures T_L and T_R, I ought to get something bounded between 0 and the Carnot efficiency.
 
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  • #2
Are you able to explain how this problem relates to thermodynamics? Where does this problem come from?

AM
 
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Related to Carnot engine acting upon another Carnot engine

1. How does a Carnot engine work?

A Carnot engine is a theoretical heat engine that operates on the Carnot cycle, which consists of four steps: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The engine works by taking in heat energy from a high-temperature source, converting some of it into work, and releasing the remaining heat energy to a low-temperature sink.

2. What is the efficiency of a Carnot engine?

The efficiency of a Carnot engine is given by the Carnot efficiency formula: 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 of a Carnot engine is dependent only on the temperatures of the two reservoirs and not on the type of working substance or the design of the engine.

3. How does a Carnot engine differ from other heat engines?

A Carnot engine differs from other heat engines in that it is a theoretical engine that operates on a reversible cycle and has the highest possible efficiency for a given temperature difference between the hot and cold reservoirs. Other real-life heat engines, such as steam engines and internal combustion engines, have lower efficiencies due to factors like friction and irreversibilities.

4. Can a Carnot engine act upon another Carnot engine?

Yes, a Carnot engine can act upon another Carnot engine. In this scenario, one Carnot engine would act as the hot reservoir for the other Carnot engine, providing heat energy to drive the second engine. However, the overall efficiency of the system would still be limited by the temperatures of the two reservoirs and the Carnot efficiency formula.

5. What are the practical applications of a Carnot engine?

Although a Carnot engine is a theoretical concept, its principles have practical applications in thermodynamics and engineering. The theoretical maximum efficiency of a heat engine is based on the Carnot efficiency formula, and real-life engines can be compared to this ideal efficiency to assess their performance. Additionally, the Carnot cycle is used as a reference cycle for the analysis of real-life heat engines.

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