# Chinese Science Bulletin, Volume 64 , Issue 5-6 : 600-609(2019) https://doi.org/10.1360/N972018-00456

## The other half of the principle of heat-work conversion cycles: The theorem, principle and core physical quantity of reversed cycles • AcceptedOct 10, 2018
• PublishedJan 25, 2019
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### Abstract

Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles.

However, it's well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance (COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows: (1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits? (2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality?

To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius' original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnot's theorem are derived and proved using the Clausius' approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.

### References

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• Figure 1

The proof of Carnot's theorem

• Figure 2

The filling factor and the average temperature of a thermodynamic cycle

• Figure 3

The T-S diagram of the air compression refrigeration cycle

• Figure 4

(Color online) The reversed Carnot cycle and an arbitrary reverse cycle

• Figure 5

The diagram of a reversed p-V cycle

• Figure 6

The proof of the theorem of the reversed cycle

• Figure 7

The p-V diagram of a reversed cycle with three work sources

• Figure 8

(Color online) The reversed p-V cycle. (a) The p-V diagram of a reversed p-V cycle; (b) the T-S diagram of a reversed p-V cycle

• Figure 9

(Color online) The T-S diagram of a reversed p-V cycle and a reversed Carnot cycle

• Table 1   Parameters of states in the reversed Carnot cycle
 压力(kPa) 体积(m3) 温度(K) 1c 6.20 28.24 609.65 2c 0.273 262.5801 250 3c 0.221 325.0269 250 4c 5.0 35.0 609.65
• Table 2   Parameters of states in the reversed cycle
 压力(kPa) 体积(m3) 温度(K) 1 5.0 23.92 416.65 2 3.0 23.92 250.00 3 3.0 35.0 365.79 4 5.0 35.0 609.65
• Table 3   The comparison of the principles of thermodynamic cycles and reversed cycles

热功转换规律

热转功(正循环)规律

功转热(逆循环)规律

输入量的品位(强度量, 状态量)

T

p

商量(比值量)(广延量, 过程量)

 $δQ/T$

$δ W/p$

功熵Sp=V

系统输出的功量通过热泵转换为热量的能力

熵(广延量, 状态量)物理意义

热熵ST

系统输出的热量通过热机转换为功量的能力

定理

卡诺定理: 工作在两个相同热源间的一切可逆循环其热效率相等

p-V循环定理: 工作在两个相同功源间的一切可逆逆循环其功效率相等

原理

不可能将热量从低温转换至高温而无其他变化

不可能将功量从低压转换至高压而无其他变化

定律

热力学第二定律(热转功的等价定律)

输入热量不能全部转化为功量,

$ηT=W net/Qin=1− T2 /T 1$

克劳修斯等式

$∮ δQ T =0$

p-V循环定律(功转热等价定律)

输入功量不能全部转化为热量,

$ηp =Q net /W in =1− p2 /p 1$

逆循环等式

$∮ δW p =0$

循环性能

两温限下卡诺循环热效率最高

两压力限下逆p-V循环功效率最大

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