1. Introduction
The first law of thermodynamics states that there is conservation in every energy conversion process, meaning that there is neither a generation nor destruction in the total amount of energy. However, nothing is stated in the law regarding the quality (nobility) of energy. Although the quest for an analytical formulation for the maximum amount of work has a long history in literature, the term exergy, first proposed by Rant [
1], is defined as the maximum possible work for a given energy transfer [
2], interacting only with the environment (known parameter) [
3]. Several authors have evaluated the applicability of the second law of thermodynamics as a decision index to improve the quality of the energy conversion process. The exergy analysis is a proper tool to evaluate different processes, ranging from biological systems [
4] to societies [
5]. Therefore, it is possible to evaluate the vestiges lost within the environment by any given process [
6].
In the past decades, the concept has been widely used by public and private institutions [
7,
8] to evaluate the efficiency of energy use of systems in various sectors, including industrial [
9,
10], transport [
11], agriculture [
12], commercial/services [
13], and residential [
14].
Similar to energy analysis, exergy analysis is a valuable tool for improving the efficiency of energy conversion processes and contributing in decision-making by identifying areas where there are higher losses of work capability or desired end product. One of the first attempts was made by Neves and Seader [
15], in which the lost work was used to evaluate efficiency parameters. Moreover, some studies used the exergy analysis to propose a different class of energy taxation [
16].
Further, the inclusion of exergy analysis in decision-making in energy planning offers advantages that go beyond the information obtained through the so-called “energy balances” [
17]. These include (i) the identification of thermodynamic limitations [
17,
18,
19]; (ii) the replacement of technologies in complex systems [
17]; (iii) the location and magnitude of the degradation of the quality of the energy (resulting from heat transfer, reaction, or other conversion process) [
17]; (iv) the adequacy between the quality of the supplied and demanded energy [
17]; and (v) information for the environmental impact analysis [
17]
Thus, in the study of energy planning, the evaluating of the life cycle of energy-intensive products and processes combined with their exergy analysis is of great interest. This application type consists of using exergy as a standard reference unit in a product life cycle assessment. The known assessment methods of this type in the literature include the Life Cycle Exergy Analysis (LCEA) proposed by Wall and Gong [
18], Ref. [
19] and the similar Exergetic Life Cycle Analysis (ELCA) submitted by Cornelissen [
20], which focuses on exergy loss during the complete life cycle of a product [
21]. There is also the cumulative exergy consumption indicator (CExC) developed by Szargut et al. [
2]. Recently, the use of parameters such as the renewable energy index has gained attention [
6]; however, there is currently no consensus in literature regarding an exergy index.
Over the past decades, there has been a systematic effort of the Brazilian governments to achieve a rational use of electrical energy for residential appliances [
22,
23]. Programs such as the “INMETRO Brazilian Labeling Program” [
24,
25], have been developed and continuously modified over time. This effort is a successful example of how simple information given to the consumer helps increasing the quality of the energy conversion in the residential sector (from grade G to A). Moreover, if all consumers were to have used, for instance, air conditioning with the top efficiency label of A, it might have been possible to achieve annual savings of 322 GWh of energy in 2007 [
25].
As discussed by Vendruscolo [
24], using electricity to heat water or to heat and cool air for refrigerators and air conditioning may account for more than 60% of the end-use of energy in Brazil. Other appliances usually found are electrical oven, electric cooktop, microwaves, lights, wash-machines [
26]. With this figure, it is essential to consider the second law of thermodynamics since the energy conversion from a source of high quality (electricity) to a grade with lower quality (heat transfer at 45–60
C) is irreversible [
27].
The energy analysis may be sufficient when there is a comparison between same types of equipment with the same energy input (air conditioning with vapor compression). Nevertheless, when there is a comparison of absorption chillers with refrigeration systems using vapor compression, there is difficulty in utilizing the performance indicator (
), since the nature of the energy input is different. Other home appliances may also be used as examples, such as electric showers, gas water heaters, or solar panels [
6].
In this article, the application of the destroyed exergy and exergy efficiency are proposed as indexes, complementary to energy efficiency or other based energy indexes. These energy based thermodynamic indicators are extensively used in Brazil [
28], e.g., in the “INMETRO Brazilian Labeling Program”. These energy indexes may be used in multiple applications from electric showers to buildings [
24,
25]. It is not the purpose of this article to criticize the First Law of Thermodynamics based indexes. Moreover, the exergy analysis is proposed to be a complementary indicator, since it is not yet generally well-known to the final consumer or to engineers. It is in the authors’ knowledge that most consumers do not buy a residential appliance based on CO
emissions nor a reduction in the monthly payments to the electrical company aiming a longterm payback. Nevertheless, as indicated by [
15,
16] it would be a purpose of the policymakers to make taxation decisions based not solely on the First Law of Thermodynamics, but also aiming the rational use of energy. This procedure may stimulate the driving factors decision making for each end costumers.
Two types of energy conversion processes are analyzed herein: water heaters and air-conditioning. A general application of this exergy analysis is offered as a basis for identification and indexation that allows end-customers to select which technology to apply to their residence. Moreover, this article intends to bring this newly modified index to the attention of policymakers in order to utilize in the best possible way the several available indexes of public policy and encourage a more careful use of energy in order to achieve the United Nations’ sustainable development goals [
29].
2. Methods
According to De Melo and Jannuzzi [
30], power performance standards begin with the “energy efficiency act” and this was adopted for cooling systems in 2007 [
26]. Based on this, two examples of energy use were analyzed from the viewpoints of the first and second laws of thermodynamics for the Brazilian scenario. Firstly, a comparison of the indexes used in literature was carried out to evaluate these cycles (
and exergy efficiency). Moreover, as stated by Vendrusculo et al. [
24], various methods of heating water by means of electrical energy account for 30% of the energy consumption of the residential sector. These technologies are labeled from the perspective of the first law of thermodynamics. All equipment is required to have these labels in order to be commercialized.
The first law of thermodynamics for a general control volume (CV) can be obtained from Equation (
1) disregarding the variation of potential and kinetic energy.
where
U is the internal energy (kJ),
is the mass flow rate (kg/s),
h is the specific enthalpy (kJ/kg),
is the heat transfer rate (kW) and
is the performed power (kW).
When the equipment is a known product, the energy efficiency may be calculated as the ratio of the desired effect to the energy input. For an air conditioning unit, it would be possible to propose an efficiency-based performance coefficient (), which is the ratio of the heat removed by the evaporator to the power of the compression. This index is usually higher than unity.
The exergy analysis for a CV can be obtained from Equation (
2), where the term
b is the exergy of a stream (kJ/kg), which is
. The exergy efficiency can be calculated by Equation (
3), which may be considered as the degradation of the quality of the energy and may be used to assess different types of household appliances [
6]. The reference choice was
C and
kPa
where
B is the exergy of the control volume (kJ),
is the mass flow rate (kg/s),
b is the specific exergy (kJ/kg),
is the exergy associated with the heat transfer rate (kW) at the surface temperature (
, in K) and
is the performed power (kW).
A primary difference between the energy and exergy analysis is the Equation (
3), which can be applied to any piece of equipment, including refrigeration systems, because these types of thermal machines require modified energy efficiency (
) to be properly evaluated. In this equation,
is the exergy of the products and
is the exergy input of the equipment.
Figure 1 shows a schematic of the National Energy Conservation Label obtained for an air-conditioning unit in INMETRO [
26]. For this type of appliance, the objective is to remove energy from the environment (the evaporator) with a certain expenditure of electrical energy (in the compressor of the system). As an example, the model “split high-wall” was chosen. The classes of grade (A being the highest grade) are: (i) A, for COP higher than 3.23; (ii) B, for COP between 3.02 and 3.23; (iii) C, for values between 2.81 and 3.02; and (iv) D, for values between 2.60 and 2.81. The complete information of the label may be seen in the references [
24,
25].
2.1. House Appliances to Heat Water for Showers
Figure 2 indicates that three primary technology methods are utilized in Brazil to heat water. It is essential to highlight that for the sake of the comparison, energy efficiency alone may not be the best tool for discriminating these three methods since the nature of the energy input is different for the same product (water with a given temperature). The electric shower is indicated in (a), gas water heater (b), and solar water heater (c). These technologies are well established in Brazil, nevertheless, electric shower is the most used.
The index used for electric shower labeling is the power consumed, ranging in grade from A to G, since, for all situations, the energy efficiency (Equation (
4)) was higher than 95%. The grade “A” was applied for power consumption lower than 2400 W and “G” for power consumption higher than 7900 W [
26]. For passage gas water heaters (also known as instantaneous heaters), the energy efficiency is defined by Equation (
5). The highest efficiencies were defined as “A” to 84%, and “E” to 76%. For solar water heaters, the index used was the average monthly energy production per square meter (
), “A” is 80.3 kWh/(month.m
) and “E”
kWh/(month.m
). The energy efficiency does not follow the same trend because there are several factors that affect system performance, such as the area and the material. In contrast, the energy produced is a more useful index, since solar energy may be considered as infinite from the perspective of human beings. Nevertheless, nothing is stated regarding the different possibilities of energy use in order to produce similar outcome.
In these equations, the terms is the enthalpy variation of the water being heated, is the electrical energy, is the heat of combustion of the natural gas. Also, is the solar irradiation multiplied by the area of the collector.
With additional information provided in the label [
26], for the sake of comparison using the same technology, these previous indexes are satisfactory in helping the consumer to select the most suitable piece of equipment (if the energy input has been decided already). Nevertheless, to compare the energy conversion qualities of these three distinct technologies, it is necessary to use another mechanism. Therefore, the exergy analysis is an analytical tool to assess the quality of the energy conversion process. The destroyed exergy for each appliance can be calculated according to Equations (
7)–(
9).
In these equations,
is the destroyed exergy of the component
i,
is the power input of the electric shower,
is the chemical exergy of the natural gas [
2],
is the exergy associated with the solar radiation [
31,
32], and
is the exergy variation of the water.
Equations (
10)–(
12) show the exergy efficiency of the appliances shown in
Figure 2, where
is the exergy efficiency of the appliance
i. These equations show the exergy efficiency, which may be used as a tool to compare different technologies of similar thermodynamic bases (meaning their work performance capability).
For solar heaters, it was considered that the average solar radiation for an inclined plan was
kW/m
[
33] and the sun temperature (
) was 5777 K.
2.2. Energy and Exergy Analysis of Air-Conditioning
Another example of the necessity of the second law of thermodynamics is demonstrated in the comparison of two different types of refrigeration cycles.
Figure 3 shows a vapor-comparison (a) and an absorption cycle (b). The prime cycle is usually found in appliances of any size from small scale residential to commercial and industrial applications. The absorption refrigeration cycle is usually applied in commercial and most industrial purposes; however, with the increased use of solar thermal heaters, this may also be incorporated into residential systems [
34]. For this investigation, both cycles were simulated based on the methods of Jabardo and Stoecker [
35] and Herold et al. [
36]. The mass, species, and energy balance calculations were carried out in order to determine the value of the same amount of energy removed from the environment,
Btu/h. Although this value was low for absorption cycles it does represent a common base of comparison in order to demonstrate the applications of the exergy efficiency. It was carried out through a comparison on the same thermodynamics basis, and a modification can be carried out to higher capacities. The exergy analysis was applied for both cycles.
In
Figure 3a,
is the power delivered to the cycle, and
is the heat removed from the environment in the evaporation process. For
Figure 3b,
, is the energy transferred in the generator to the absorption cycle.
For the vapor-compression refrigeration cycle (
Figure 3a), the coefficient of performance (
) and the exergy efficiency are evaluated according to Equations (
13) and (
14). It was possible to infer from these equations that both can be used to discriminate between the devices. However, Equation (
14) gives the highest value of 100%, whereas the Equation (
13) can achieve values of COP higher than unity, considering that it compares heat removed from the environment,
(lower quality) with electric power,
(higher quality). Being the maximum value, on an energy basis, the Carnot Performance Coefficient (COP). This fact may lead to some misleading information when there is a comparison of different technologies. Nevertheless, since the exergy analysis uses physical quantities of the same nature (maximum available power), e.g., in a heat transfer, there is always an exergy associated to its potential of performing any kind of work. Moreover, if we analyze this useful effect more carefully, it is possible to conclude that the while heat is removed from the environment from the evaporator, the exergy is transferred to the environment (increase the disequilibrium with the reference ambient) as discussed in [
37].
The absorption conditioning systems (usually available as chiller),
Figure 3b, can be evaluated according to its COP (Equation (
15)). This value is usually lower compared to the one related to vapor compression cycles, since this type of chiller compares the energy of the same quality (heat transfer rate). As in, it compares the heat provided in the generator with the heat removed from the environment (usually
is smaller than other types of energy transfer).
Equations (
14) and (
16) represent the ratio of the same quality (exergy). In the denominator, the quality of the heat in the generator,
, and real power is provided in the compressor (
). Whereas, in the numerator of both equations, there is the exergy transfer associated with the evaporation process,
. With exergy efficiency, it was possible to compare two distinct technologies. This index can be used to assess the energy conversion process in a rational manner. Therefore, it may constitute a complementary index to the
, in order to help the customer decide which technology to invest in.
The two systems were simulated operating at an evaporation temperature (
) of 3
C and rejected heat to the environment at 25
C (
). The temperature of the absorption cycle generator (
) was set to 80
C. In order to best compare both cycles, the destroyed exergy was shown as a percentage of the exergy input, e.g., for the compression system, the input was
and the input of energy in the evaporation cycle was
. The terms
and
were zero, since
.
4. Conclusions
In this article, a simple idea was proposed in the Brazilian context to complement the labels of Procel and the National Energy Conservation Label [
26] programs that were designed based on principles of the first law of thermodynamics. The purpose was to incorporate the usage of the second law of thermodynamics to help increase the capability of the consumer to discern which technology may have a higher exergy demand and environmental impact.
This investigation found that the exergy analysis provided the true losses of an energy conversion process and therefore has the potential to be used as a tool to quantify multiple methods for obtaining a similar outcome. It was demonstrated from the exergy analysis that the indexes converged into proximity values, around 3%.
For refrigeration systems, it was demonstrated that the exergy analysis can be used to carry out comparisons for residential, commercial, and industrial appliances. In this experiment, a low thermal load (12,000 btu/h) was used to compare residential appliances (even if the absorption cycle did meet this demand); nevertheless, a basis of thermodynamic investigation is proposed for carrying out future reports. Moreover, it may be preferable to use absorption refrigeration cycles depending of its initial costs. A more detailed analysis may be carried out, since the price of split-highwall is very attractive, and the demand of the absorption cycle must be higher than those indicated in this article.
Complimentary future research that may be considered might include investigations into how humans use natural resources and how the changes in our habits and public policies may be a basis from which we can achieve a more sustainable society as outlined by [
29]. Therefore, public policies may be a basis for the way energy and natural resources are used in the nation, bearing in mind that the use of the electrical shower accounts for 30% of electricity consumption in Brazilian households [
24].
The reason for this article is to propose an additional tool for policies-making and decision buyers. That the quality of the energy may lead to better resource usage, and even a fast payback time, based on the second law of thermodynamics. To understand the consumption of electrical shower, most citizens may compare with the number of lamps, for instance. Yet, this is a case study in Brazil, with its own realities and differences in education. Therefore, the information A to G of quality of energy use would be adequate to facilitate the consumer.