Optimizing Heat Rejection in Cyclic Heat Engines: A Case Study

Introduction

In the context of thermodynamics, a cyclic heat engine operates between a high temperature and a low temperature to perform useful work. This article focuses on a specific case where a heat engine operates between 800°C and 30°C. Understanding the principles and calculations involved in the least heat rejection per kW net output is crucial for optimizing engine performance and efficiency.

Cyclic Heat Engine Operation

A cyclic heat engine, such as the one operating between 800°C and 30°C, follows a series of processes to convert heat into useful work. The engine absorbs heat from the hot reservoir, performs work, and rejects the remaining heat to the cold reservoir. The efficiency of the engine is a key factor in determining the amount of heat rejected per kW of net output.

Maximum Efficiency and Heat Rejection

The maximum efficiency (η) of an ideal thermodynamic engine (such as a Carnot engine) can be calculated using the formula:

[eta 1 - frac{TL}{TH}]

Where:

TH is the temperature of the hot reservoir (800°C or 1073K) TL is the temperature of the cold reservoir (30°C or 303K)

Substituting the values, we get:

[eta 1 - frac{303}{1073} 0.7176 text{ or } 71.76%]

This efficiency implies that the engine would reject heat at a rate of:

[frac{1}{eta} - 1 frac{1}{0.7176} - 1 0.3935 text{ kW per kW of net output}]

Carnot Engine Efficiency and Least Heat Rejection

The Carnot engine, being an ideal thermodynamic engine, operates with the highest possible efficiency for a given temperature range. For the given temperatures, the efficiency can be calculated as:

[eta 1 - frac{300}{1200} 0.75 text{ or } 75%]

This higher efficiency allows the engine to operate with less heat rejection per kW of net output. Specifically:

[frac{1}{0.75} - 1 frac{4}{3} - 1 frac{1}{3} text{ kW per kW of net output}]

Therefore, the least heat rejection is achieved by an ideal Carnot engine, which operates with a higher efficiency.

Conclusion

Understanding the principles of heat rejection in cyclic engines is crucial for optimizing engine performance and efficiency. By utilizing the high efficiency of an ideal Carnot engine, the engine can operate with less heat rejection per kW of net output, leading to improved overall performance and reduced environmental impact.

Keywords: cyclic heat engine, Carnot engine, heat rejection optimization, thermodynamic efficiency, engine performance