# Energy Units

### Joule

The joule (J) is a SI derived unit for measuring energy, and the related mechanical work and heat [1]. The joule in SI base units is 1 J = 1 kg⋅m^{2}⋅s^{-2} which is equivalent to the newton-meter (N⋅m) and the watt-second (W⋅s) [1].

A good way to visualize an amount of energy is to look at it in terms of gravitational and kinetic energy.

- Convert energy to height in Earth's gravity using h = E/(mg) and a sample mass like 1 g, 1 kg, or 1 000 kg.
- Convert energy to speed using v = sqrt(2E/m) and a sample mass.

For example, 1 joule is not a lot, as it is only enough to lift 100 grams by about 1 meter, or the kinetic energy of a 100 gram object moving at 6 m/s [1]. Similarly, 1 kilojoule is enough to lift a 100 kg weight by 1 meter, and to launch a 5 g object at 632.5 m/s.

Heating water is very energy intensive due to its high specific heat capacity. For reference, raising the temperature of 1 L of water by 1 degree Celsius takes 4 184 J, bringing 1 L of water from room temperature (22°C) to boiling (100°C) takes about 1.46 MJ, and fully evaporating that litre would take an additional 2.26 MJ due to latent heat of vaporization [2].

The main unit of energy for measuring electricity consumption is the kilowatt-hour (kWh), which is equivalent to 3.6 MJ. In Ontario, current electricity prices vary between 8 to 18 cents per kWh [3]. The average household in Ontario consumes around 600 to 800 kWh per month or 2.16 to 2.88 GJ per month [4]. In terms of batteries, which convert chemical energy to electrical energy, an alkaline AA battery stores about 9 kJ of energy, a large smartphone battery of 5000 mAh at a nominal voltage of 3.7 V translates to 66.6 kJ, and the average electric car battery stores about 60.4 kWh or 217.4 MJ [2][5].1

### Joule per Kelvin

Joule per kelvin (J/K) is a SI derived unit for measuring entropy (S) [6]. Joule per kelvin in SI base units is 1 J/K = 1 m^{2}⋅kg⋅s^{−2}⋅K^{−1}[7]. Entropy is a measurable physical property this is most commonly associated with a state of disorder, uncertainty and randomness. The concept is widely used in fields such as thermodynamics and statistical physics [7].

Systems tend towards higher values of entropy. We can visualize this using an example such as a melting ice cube. An ice cube is a solid that is very structured and ordered with low entropy. If left at room temperature, over time the ice cube will melt into into water which has a higher entropy compared to an ice cube due to the randomness of the liquid structure. if this liquid water is then boiled, the water will become a gas that has an even higher entropy than both water or ice due to the randomness of gaseous structures [8].

An analogy to further help understand entropy is to consider a bedroom. Over time, this bedroom will become messier and disorderly, tending towards higher entropy. To counter this, work must be put in to clean the room and make it more orderly, lowering the entropy of the room [9].

[9]

### Joule per Kilogram-Kelvin

Joule per kilogram-kelvin (J/(K·kg)) is a SI derived unit for measuring specific heat capacity [7]. Joule per kilogram-kelvin in SI base units is 1 J/(K·kg) = 1 m^{2}⋅s^{−2}⋅K^{−1} [7]. Informally, specific heat capacity is the amount of heat required to increase one unit of mass by one unit of temperature. For example, the heat required to raise 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J/(K·kg) [10].

Heat capacity varies with temperature and is different for each state of matter. An example of this is looking at the states of water. Liquid water has a high heat capacity of about 4184 J/(K·kg) at 20°C while ice at just below 0 °C is only 2093 J/(K·kg) [10].

### Joule per Cubic Metre

Joule per cubic metre is a SI derived unit for measuring energy density. Joule per cubic metre in SI base units is 1 J/m^{3} = 1 m^{−1}⋅kg⋅s^{−2} [11].

Energy density is the amount of energy stored in a given system or region per unit volume. Energy density shares the same units as pressure and is a synonym in many cases. An example of this would be a magnetic field. the energy density of a magnetic field may be expressed as, and behave as, a physical pressure [11].

Depending on the material and the process, energy density can greatly vary. For example, in material deformation, a rubber band has energy density ranging from 2,200 to 8,900 (J/L), in chemical reactions, gasoline has an energy density of 34.2 (MJ/L) and in nuclear reactions, Plutonium 239 have an energy density ranging from 490 (TJ/L) to 1.7 (PJ/L) [11].

### References

[1] “Joule,” *Wikipedia*, 06-Apr-2021. [Online]. Available: https://en.wikipedia.org/wiki/Joule. [Accessed: 14-Apr-2021].

[2] “Orders of magnitude (energy),” *Wikipedia*, 08-Apr-2021. [Online]. Available: https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy). [Accessed: 14-Apr-2021].

[3] “Historical electricity rates,” *Historical electricity rates | Ontario Energy Board*. [Online]. Available: https://www.oeb.ca/rates-and-your-bill/electricity-rates/historical-electricity-rates. [Accessed: 15-Apr-2021].

[4] A. Fremeth, “A closer look at household energy bills in Quebec and Ontario,” *Ivey Business School*, 13-Jun-2019. [Online]. Available: https://www.ivey.uwo.ca/energycentre/blog/2019/06/a-closer-look-at-hydro-quebecs-electricity-price-advantage-over-ontario/. [Accessed: 15-Apr-2021].

[5] “Useable battery capacity of full electric vehicles,” *EV Database*. [Online]. Available: https://ev-database.org/cheatsheet/useable-battery-capacity-electric-car. [Accessed: 15-Apr-2021].

[6] I. eFunda, “Home,” *eFunda*. [Online]. Available: https://www.efunda.com/glossary/units/units--entropy--joule_per_kelvin.cfm. [Accessed: 23-Jul-2021].

[7] “SI derived unit,” *Wikipedia*, 25-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/SI_derived_unit. [Accessed: 23-Jul-2021].

[8] “What is an example of entropy from everyday life?: Socratic,” *Socratic.org*, 12-Apr-2014. [Online]. Available: https://socratic.org/questions/what-is-an-example-of-entropy-from-everyday-life. [Accessed: 23-Jul-2021].

[9] Anonymous, “What is an example of entropy in everyday life?,” *Quora*. [Online]. Available: https://www.quora.com/What-is-an-example-of-entropy-in-everyday-life. [Accessed: 23-Jul-2021].

[10] “Specific heat capacity,” *Wikipedia*, 13-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Specific_heat_capacity. [Accessed: 23-Jul-2021].

[11] “Energy density,” *Wikipedia*, 16-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/Energy_density. [Accessed: 26-Jul-2021].

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