Question

(I) A heat engine's high temperature $T_H$ could be ambient temperature, because liquid nitrogen at 77 K could be $T_L$ and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen "fuel"(Fig.15$-$25)? FIGURE 15-25 Problem 22. (CANT COPY FIGURE)

Name: Problem 22, Chapter 15: Physics: Principles with Applications
Uploaded: 2019-04-30T22:52:00-08:00
Duration: 1 min 10 s
Channel: Averell Hause
Description: (I) A heat engine's high temperature TH could be ambient temperature, because liquid nitrogen at 77 K could be TL and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen "fuel"(Fig.15-25)? FIGURE 15-25 Problem 22. (CANT COPY FIGURE)

   (I) A heat engine's high temperature $T_H$ could be ambient temperature, because liquid nitrogen at 77 K could be $T_L$ and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen "fuel"(Fig.15$-$25)?
FIGURE 15-25 Problem 22. (CANT COPY FIGURE)

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition

Chapter 15, Problem 22

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Solved by Expert Averell Hause

04/30/2019

Step 1

Step 1: The efficiency of a Carnot engine is given by the formula: \[ \eta = 1 - \frac{T_L}{T_H} \] where $T_L$ is the low temperature and $T_H$ is the high temperature. Show more…

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(I) A heat engine's high temperature $T_H$ could be ambient temperature, because liquid nitrogen at 77 K could be $T_L$ and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen "fuel"(Fig.15$-$25)? FIGURE 15-25 Problem 22. (CANT COPY FIGURE)

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Key Concepts

Carnot Efficiency

Carnot efficiency is the theoretical maximum efficiency that any heat engine operating between two thermal reservoirs can achieve. It is defined by the formula ? = 1 ? (T_L/T_H), where T_L is the absolute temperature of the cold reservoir and T_H is the absolute temperature of the hot reservoir. This concept is fundamental to understanding the limits imposed by the second law of thermodynamics on energy conversion processes.

Absolute Temperature Scale (Kelvin)

Using the absolute temperature scale (Kelvin) is crucial in thermodynamics, particularly in calculations like the Carnot efficiency, because it provides a scale where zero represents absolute zero, ensuring that temperature ratios are meaningful in energy conversion calculations. This avoids the inconsistencies that would arise from using relative temperature scales such as Celsius or Fahrenheit.

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