To convert the final exergy values obtained in the previous steps to useful exergy values, second law efficiencies are required. The major part of the second law efficiencies depend on the first law efficiencies and on the end-use device type. In [
7,
8], the useful exergy values were calculated using second law efficiencies that depended mainly on the end-use category and not on the energy carrier. In our study, efficiencies are computed for the energy carrier (end-use pairs), in order to obtain more accurate results. A brief explanation of the second law efficiencies used is given for each end-use category.
2.3.1. Heat
To estimate second law heating efficiencies, service and environment temperatures and first law efficiencies are needed,
η:
In this paper, first law efficiencies are estimated by energy carrier, instead of using generalized first law efficiencies for all of the heat processes from all of the energy carriers. The carrier-specific first law efficiencies used by [
16] for the European Organization for Economic Co-operation and Development (OECD) countries are used, divided between low, medium and high temperature heat. The energy carriers available for the disaggregation are coal, renewable fuels, oil, natural gas and heat. The evolution of first law efficiencies was assumed equal to the evolution of heat efficiencies used by [
7,
8].
The service temperatures defined for the heat processes are shown in
Table 2. To estimate the second law efficiency for space heating uses, we considered the average winter temperature used by [
7] for Portugal. The annual average temperature is 15.4
C , and the that of the winter is 9.8
C.
The second law efficiency of low temperature heat uses was multiplied by the exergy allocated to this end-use to obtain useful exergy. The allocation for this end-use in the residential, service and miscellaneous sectors (domestic water and space heating) follows from the assumptions that were mentioned in
Section 2.2. Some of the energy carriers used in these sectors, such as “peat briquettes”, are fully allocated to this end-use (for further details, see the
Supplementary Materials), while in the case of electricity, only a fraction (dependent on time) is used for this purpose.
2.3.2. Transport
For gasoline engines, the theoretical maximum efficiency depends on the compression ratio,
r, and the specific heat ratio,
γ, as shown in Equation (
2).
The evolution of the compression ratio of gasoline engines during the time span, obtained from [
7,
17], is used to estimate the theoretical maximum efficiency of these engines. The real (first and second law) efficiency is given by Equation (
3), in which the coefficients
denote losses, which are described in
Table 3 (based on [
17,
18,
19]).
In previous studies ([
8,
20]), a loss coefficient of
due to accessories (such as air conditioners (AC)) was included. Here, a different approach is followed, where AC is accounted for directly within LTH or cooling.
Gasoline engine efficiency was used as a starting point to estimate the efficiencies of the other energy carriers used for transport and types of transportation, shown in
Table 4. As mentioned in [
21] and for the same compression ratios, the efficiency attained in ideal Otto cycles is effectively greater than the efficiency obtained in ideal diesel cycles. However, diesel cycles have greater compression ratios, therefore achieving higher efficiencies. The estimated difference is a 25 percent higher efficiency for diesel engines [
18]. The values of the efficiencies can be found in the
Supplementary Materials.
2.3.6. Cooling
In previous papers (namely [
8,
20]), the end-use category for SMD comprised refrigeration, HVAC and cooling devices. A different approach is followed in this paper, taking into account that the real end-use for cooling devices is the cooling of spaces or goods. The previous approach was based on the fact that the electricity is used to power a mechanical movement, such as the rotor in electric motors, or in the case of refrigeration and air conditioning, the compressor and fans, which come under the category of the mechanical drive. However, for refrigeration and air conditioning, the mechanical movement of the compressor is not the end-use. This is an inconsistency in the method used when addressing refrigerators and air conditioning as a stationary mechanical drive and not space heating/cooling.
In this paper, a new category of end-use is created to fix this issue: cooling. The shares of electricity allocated to cooling devices (comprising refrigeration and air conditioning) were retrieved from [
15], with estimates for cooling and heating uses for air conditioners. These data are for the USA, and shares for the residential sector are shown in
Figure 2. The electricity shares were extrapolated at constant values from 2001 to 2010, because we did not have data regarding this period, and there was no marked tendency regarding the evolution of these shares between 1980 and 2000. The relative importance of exergy consumption for refrigeration systems has been decreasing, although the absolute values have been increasing. However, the use of air conditioning devices has grown to a 15 percent share of electricity consumption in the residential sector.
Air conditioning from electricity is allocated both to cooling and low temperature heat (space heating during winter), and refrigeration uses from electricity are included in the category `cooling’. Air conditioner uses in cars for heating and cooling are also considered, with heating uses (during the winter season) going to the LTH uses and cooling uses (during the summer season) going to the cooling category.
Conversion second law efficiencies for refrigeration and air conditioning end-uses were studied. Refrigerators and air conditioners are quite similar in the working principle and use the same components. The difference relies on refrigerators being enclosed and insulated volumes [
15]. Analyzing the cooling and heating devices from a thermodynamic perspective, the coefficient of performance is the first law efficiency indicator.
In
Table 5, the coefficients of performance (COP) for cooling and heating devices are shown. For cooling,
is the heat removed from the space being cooled, and
is the electricity required to power the chiller or compressor. Extracting heat from an enclosed volume to maintain its temperature at
, with an environmental temperature of
, has the ideal COP expressed in
Table 5. In heating, the final use desired is to provide heat at a temperature
in an environment with a colder temperature
. It is important to correctly define the environmental temperatures for summer and winter, for space climatization, as done in [
27], because second law efficiencies for cooling and heating depend on them. The heating exergy efficiency in Portugal when a heat pump is used will vary from that of Norway, even if the same technology is involved, because of the different value used for the winter reference temperature, emphasizing that the best solution might not be the same for all countries.
Typical values for the COP of electrically-driven air conditioners and refrigerators are in the range of two to four [
28]. Second law efficiencies, needed to convert final exergy values into useful exergy values, are shown in
Table 5.
Values for the environment temperature and the temperatures of the hot and cold air are presented in
Table 6, for Portugal. Data are divided between heating and cooling uses, with the outdoor temperature being the winter temperature for the heating uses and the summer temperature for cooling uses, taken from [
13,
29]. The indoor air temperatures were taken from the Portuguese legislation for the comfort temperatures for AC in buildings (Regulamento das Características de Comportamento Térmico dos Edifícios (RCCTE) in Decreto de Lei n80/2006 de 4 de April 2006 [
30]).
For refrigerators, efficiency is calculated assuming a 1/3 load from the freezer box at −15
C and a 2/3 load from the cooler box at 4
C [
2].
After applying the mean efficiencies from final to useful, the total useful exergy is then aggregated into different categories according to useful exergy uses, as shown in
Table 2.