What is the efficiency of a Carnot engine and the effectiveness of a heat pump?

In summary, a Carnot engine uses hot and cold reservoirs at temperatures of 1684 K and 842 K, respectively, with input heat of |QH| and work delivered to operate a Carnot heat pump. The heat pump removes heat from the 842-K reservoir and transfers it to a hot reservoir at temperature T`. The input heat for the engine is twice the amount of heat removed by the heat pump. The efficiency of the engine can be expressed as W = QH - Qc, and the effectiveness of the heat pump can be found by inputting W to transfer QH to another reservoir at temperature T'. The temperature T' for the hot reservoir can be calculated as 1263 K.
  • #1
sora1607
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Homework Statement



A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is |QH|. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir at a temperature T`. The amount of heat removed from the 842-K reservoir is also |QH|. Find the temperature T`.


Homework Equations



Qc/Qh = Tc/Th
Qh = W + Qc

The Attempt at a Solution


This problem was posted before with no solution and now I'm running into the same problem. I've attempted the problem by first getting Qh=2Qc for the carnot engine. Then this input heat + W is used to operate a heat pump. So I got Qh + w = 2Qc. I'm stuck starting here. I'm not sure how this input heat would fit into the heat pump cycle.

The answer is suppose to be 1263
 
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  • #2
For the Carnot Engine section, how do you find the efficiency of the engine? (express W in terms of Qh).

For the heat pump section, we are inputting W to move Qh to some other reservoir Q (at temp T'). How do you find the effectiveness of a heat pump?
 

FAQ: What is the efficiency of a Carnot engine and the effectiveness of a heat pump?

What is a Carnot engine problem?

A Carnot engine problem is a theoretical problem in thermodynamics that involves finding the maximum possible efficiency of a heat engine operating between two given temperatures. It was first studied by French physicist Nicolas Léonard Sadi Carnot in the early 19th century.

What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. It is used to model the operation of an ideal heat engine.

What is the efficiency of a Carnot engine?

The efficiency of a Carnot engine is given by the ratio of the difference in temperature between the hot and cold reservoirs to the temperature of the hot reservoir. It is often expressed as a percentage and represents the maximum possible efficiency that a heat engine can achieve.

What are the assumptions of the Carnot engine problem?

The Carnot engine problem assumes that the engine operates in a reversible manner, meaning that there is no friction or other forms of energy loss. It also assumes that the working fluid is an ideal gas and that the engine operates in a closed cycle with a constant amount of gas.

How is the Carnot engine problem solved?

The Carnot engine problem can be solved using the Carnot cycle and the principles of thermodynamics. The efficiency of the engine can be calculated based on the temperatures of the hot and cold reservoirs, and the work and heat transfer at each stage of the cycle can also be determined.

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