## Energy

# Notes by R.Oliva / revised by G. Dutt 07-2024 – Alternative Energies Area (AEA) UNPA - ITA - CIT Santa Cruz

#### 1. BASIC CONCEPTS OF ENERGY, POWER AND EFFICIENCY - (Download as PDF document)

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1.1 BASIC DEFINITIONS: It is necessary to know some energy concepts, from a physical or engineering point of view. Its formal definitions allow us to introduce the topic. The infographic in Figure 1 gives the definition of energy, its units and characteristics, and an example that shows two of its forms (potential and kinetic energy).

Energy is conserved and its forms are equivalent (Figure 2 ), although the conversion between these forms is not always feasible. In general, the conversion always entails that a portion is dissipated into the environment as thermal energy (“losses”) and its recovery into useful energy, due to the reduced temperature difference, is technically complex and expensive.

1.2 WORK AND ENERGY: Lifting a box requires a specific amount of energy E, which is comparable to the work required. This energy is measured in Joules [J], a unit derived from the International System of Units or SI [SI-Wiki, 2024] [SI-Wiki-d, 2024]. To perform the task ( Figure 3 ), the same amount of energy will be required whether the box is lifted quickly or slowly.

## Figure 3

To lift the box faster, we need to increase the power P, that is, the change in energy over time. This is precisely expressed mathematically as (Eq.1):

and its unit, the Watt [W] (or watt), is equivalent to one [J/s].

In an expression of mechanical physics, work is equivalent to the product of a force F (expressed in newton[N]) by a distance d, expressed in meters [m] therefore the unit of E is [Nm]=[J]. (Note that it has the same units as torque [Nm], although it is a different physical phenomenon.) A very important relationship, which arises from Eq. 1 and which links energy, power and elapsed time, can be seen with an example in Figure 4 . Mainly when it comes to electrical energy, the product of the power P times the elapsed time Dt is what is usually called the energy consumed (or delivered) in that period Dt, and the most common unit is [Ws] or watt-second, which is the same as Joule. For electrical energy in particular, the use of Wh or watt-hour is preferred. In large quantities, it is common to use the prefixes k (x 1,000) or M (x 1,000,000).

## Figure 4

The relationship that arises from the example in Figure 4, and which refers to an energy (in this case consumed by an electric iron) in a given period D t operating at a power P can then be written in this way (Eq.2) :

Note that this is a PRODUCT and is NOT W/h or kW/h, units that would express a variation or change in power over time.

The other important relationship is efficiency (often expressed with the Greek letter “eta” or h ) which is the relationship between the “useful” output power Pout and the input power (“demanded or consumed”) Pin in a device or machine. Over the same period of time, this is equivalent to the ratio of output energy to input energy. It should be noted that it is a dimensionless magnitude, with a value between 0 and 1 or in percentage notation, between 0 and 100% (Eq.3)

An efficiency of 100% is unattainable within the theoretical limits of current physics, although many devices reach very close values. On the right in Figure 4 is an extreme case of a fictitious electric motor whose useful mechanical power on the shaft is 50 W, and the electrical power it demands is 100 W, which results in a ratio of 0.5 that is, an efficiency of 50% (Typically, the efficiency of an industrial three-phase asynchronous motor exceeds 90%).

2. PREFIXES AND UNITS

When studying the topic of energy, as we saw, physical concepts appear that we must know. Their precise representation is an important issue, which is why we dedicate this section to units and their prefixes.

2.1 PREFIXES: Prefixes indicate multipliers that make numbers more “manageable” in the representation of physical units. For example, it is more practical and understandable to say that a power plant has a power of 100 MW (one hundred megawatts) than to say that it has 100,000,000 W (one hundred million watts) even if the value is identical. The SI is an international agreement in constant updating [ISO-80000-1,2022] on the standard units to be used, their definitions and the names of these prefixes, which are shown in Figure 5. The scheme of using multiples and submultiples of 10 to represent various quantities was adopted. It should be noted that the prefixes apply to all units, not only related to energy. For example, the speed of light is 30 cm/ns (30 centimeters per nanosecond).

## Figure 5

The upper part (I) corresponds to the multiples, and continuing with the example for the derived unit “power”, Table 1 shows its typical application.

Note that the prefixes in capital letters are multiples greater than one thousand. It is important to note that “kilo” (mil) is denoted by the lowercase k, to differentiate it from the base unit K (Kelvin) of temperature (see 2.2). Therefore, it is incorrect to write kilowatt-hour as KWh. The correct form is kWh.

To represent small quantities, submultiples are used (II in Figure 5), parts less than one that can be seen at the bottom of Figure 5. These involve multiplying by 10 with negative powers, for example for the base unit meter (m). the hundredth part is known as the cm or centimeter (multiply times 1E-02 = 1/(10*10) = 1/100 = 0.01 m, two zeros to the left of the decimal symbol). Similarly, the millimeter or mm involves dividing cm by 10 (for the meter it is a multiplier times 1E-03 = 1/(10*10*10) = 1/1000 = 0.001 m, three zeros to the left of the decimal symbol).

2.2 UNITS: The SI base units can be seen in Figure 6 and some of the derived units (which were mentioned in Part 1) in Table 2. A very useful free infographic on base and derived units is available free in [NIST SI Base Units Relationships Poster, 2020]. Although the origin of the base units, the associated constants and the way to replicate the measurements are detailed in the ISO/IEC 80000 Standard, with versions for different branches of physics and technology, there are guides on recommendations for shape and its historical evolution such as [NIST- The International System of Units (SI), 2019], and others that constitute practical use guides such as [NIST Guide for the Use of the International System of Units (SI), 2008] that are free. In these guides it is possible to find units not included in the SI but accepted in their use (hour, minute for example) and there are conversions to historical units (psi, foot, calorie, BTU) that are still widely used in the industry.

Knowledge of energy issues, and the associated calculations, requires the management of many of these physical units and their correct expression. The advantage is universality and uniformity across languages and countries globally, which is important given the economic and strategic value of energy exchanges.

REFERENCES

[ISO-80000-1,2022] ISO 80000-1:2022 Quantities and units https://www.iso.org/obp/ui/en/#iso:std:iso:80000:-1:ed-2: v1:en

[SI-Wiki, 2024] International System of Units: https://es.wikipedia.org/wiki/Sistema_Internacional_de_Unidades

[SI-Wiki-d, 2024] Units derived from the International System: https://es.wikipedia.org/wiki/Unidades_derivadas_del_Sistema_Internacional

[UC-Energy Education, 2017] Energy vs power: https://energyeducation.ca/encyclopedia/Energy_vs_power

[NIST- The International System of Units (SI), 2019] https://www.nist.gov/pml/special-publication-330

Or in PDF: https://doi.org/10.6028/NIST.SP.330-2019

[NIST Guide for the Use of the International System of Units (SI), 2008] https://www.nist.gov/pml/special-publication-811

[NIST SI Base Units Relationships Poster, 2020] https://doi.org/10.6028/NIST.SP.1247