Grzegorz Karwasz

1. Grzegorz Karwasz University Nicolaus Copernicus Didactical material: Secondary School Part V: „Energy”

2. Energy: the origin of the term • 2/15 The term „energy” comes from Greek „energeia”, ένέργεια that was used by Aristotle (in his Metaphysics) and had the meaning of act, being, becoming, differently to potenzia that was only the possibility of being. Modern understanding of energy was formed at about half of XIX century, with works by Carnot, Joule and others, who showed that the mechanical work can be converted into heat: so also the heat is a form of energy. In fact, looking into description of „nutritional value” of any food (next page), we find the values both in „joules” that is the unit for work and the mechanical energy and „calories” (or rather kcal) that is the old unit for the heat.

3. Joule: Energy is the ability of a system to perform the work Piłeczki, proca magnetyczna Westminster Abbey, Joule’s tomb The energy contents

4. ένέργεια (Aristotle) • Metaphysics: act = state, action, actuation, performing, implementation

5. Ep + Q Ek M h Ep= (m+M)gh Ek= mv2/2 • Energy: definition • 3/15 The discussion on the exact definition of energy is a kind of „never ending story”. The current consensus is, however, that The energy is the capacity of a body to perform work. For example, the kinetic energy of a bullet hitting so- called ballistic pendulum like in the figure, causes the block to rise (and a part of the kinetic energy changes into the heat.) In the second experiment, the circus loop with radius R, the potential energy of the ball at the beginning of the rail transforms, in the highest point of the loop into the kinetic energy, and a part is still the potential energy. E=5mgR/2 E= mv2/2 + 2mgR

6. Energy: Types • 3/15 • We distinguish two types of the mechanical energy: • the one related to the motion, called kinetic energy, Ek= ½ mv2where m is the mass of the moving object and v is its velocity • the one related to the elevation of the body, called potential energy, Ep=mgh, where h is the height of the elevation and g is the gravity acceleration • It is called also potential energy the energy stored in a spring. If the spring is harmonic, i.e. the force needed to keep it at a distance x from the equilibrium position is F=kx (with k – elasticity constant), the potential energy of elasticity amounts to Ep= ½ kx2. • In general, the energy related to the position is called potential energy. For the electro-static fields the potential energy of two point charges, q and Q positioned (in vacuum) at a distance of r is Ep=(1/4πε0) qQ/r ,with ε0 being the dielectric permeability of vacuum.

7. Energy: Carriers and transformations • 3/15 • As discussed earlier, the energy can appear in different forms. • Practically, we must distinguish different carriers of energy: • solar radiation • electric currents • geothermic heat • kinetic energy of the wind • chemical energy of hydrogen • etc. Hans. U. Fuchs, Hydrogen and Fuel Cells. How, What for, and Why? Didactical Materials FCHGo, 2019

8. Energy: Constraints • 3/15 As already seen from the previous pages, the potential energy (of a body in Earth’s gravitational field, but also pf a spring) requires the definition of „zero-height” point: a body falling from a hight to the zero level acquires the kinetic energy. Does the kinetic energy require also a point of reference? From the times of Einstein we know that yes! The velocity is not an absolute value: it depends on the references frame: a body can posses the kinetic energy in one system of reference and in another, i.e. moving with the same velocity that itself – may have the zero kinetic energy. So, coming to the very definition of the energy – depending on the system of reference (i.e. the point defined as „zero energy”) the capacity of performing the work can vary: even if the system apparently possesses the energy, the useful work can be null. We discuss this point, in order to introduce the thermodynamics.

9. Energy & Heat • 3/15 The concept of energy was established only when Joule showed the equivalence of the heat and work. This observation leads to the first* principle of thermodynamics: The work performed on a system W and the heat Q transferred to the system give a rise to the internal energyU of the system. ΔU = W + Q Additionally, it is clear that the heat can be transferred only from the body with higher temperature, say T1, to the body with lower temperature, say T2. This puts immediately limits on the efficiency of thermodynamic machines, as shown later, *The zeroth principle says tha the heat flows from a hotter to a colder body.

10. Heat & Temperature • 3/15 What temperature is? Explaining to children we would say: „What we fell hot or cold by our hand”* Obviously, we can not define it in this way in physics. The temperature is a measure of the internal energy of the body. U ~ T , where the sign of proportionality ~ needs some explanations: the constant of proportionality depends on the internal (i.e. atomic) structure of the body. It is easiest to explain it for so-called perfect gases, i.e. gases that can be approximated as small, hard, colliding spheres. Noble gases are a good approximation. The internal energy means that the body accumulates energy: this must be a mechanical energy of its atoms (or molecules). *Our hand (heat receptors) capture the thermic movement of atoms, giving the sensation of the temperature. For more specific definition see also Fuchs, 2019, op. cit.

11. Heat engines • 3/15 The principle of equivalence between the mechanical work and the heat allows thermic engines to work: as the mechanical energy can be transformed to the heat (like in the experiment by Joule), also the heat can be transformed into the mechanical work (what is equivalent to the mechanical energy). But as the mechanical energy can be fully transformed into the heat (in the friction, for example), not the whole heat absorbed Q1 by the system can be transformed into the mechanical work. A part of the heat, Q2 must be released to the environment. In the ideal heat engine the efficiency η is the ratio between the heat used, i.e. Q1-Q2 and the heat absorbed η = (Q1 – Q2) / Q1 As in gas engines the heat is proportional to the gas temperature, the efficiency (of an ideal engine) amounts to η = (T1 - T2) / T1. where T1 is the temperature of the heat source and T2 – of the radiator (i.e. the heat sink). So, the efficiency rises if the heat source is hotter and the cooler – colder.

12. Heat engines • 3/15 What could be the „highest” energy efficiency of a thermodynamic engine according to the law? η = (T1 - T2) / T1. „ The 605 MW General Electric 9HA achieved a 62% efficiency rate with temperatures as high as 1,540 °C The efficiency of a conventional car engine is only some 30% The rest goes directly into heat, not saying about CO2 emission. https://www.ge.com/power/gas/gas-turbines/9ha

13. Hydrogen fuel cell The idea of the fuel cell is that it is an engine: supplying hydrogen H2 and oxygen O2 one produces the electrical current and the two gases form water H2O. From the point of view of energy, the chemical energy of the two gases converts into the electrical energy. The efficiency of a fuel cell is much higher (up to 80%) than of a combustion engine. But thermodynamics says that also the heat must be produced (see lesson No.4).

14. „Ideal” hydrogen fuel cell The detailed scheme of energy transformations is as shown here The chemical level of H2O is lower than that of H2 and O2 separately. The fall of the chemical energy level pumps-up the electrical charge to a higher (by approx. 1 V) potential, making the electrical current flow. Hans Fuchs, op. cit.

15. Real hydrogen fuel cell In a real hydrogen cell the heat losses are also present • These loses come from several sources: • the activation potential (a bias of the proton-exchange membrane) • internal resistance of the cell (ohmic losses) • additional losses, due to technical imperfections. • In overall a 80% theoretical efficiency is still a far goal. Hans Fuchs, op. cit., p. 27

16. Real hydrogen car In practice, 50% efficiency would be already excellent https://www.researchgate.net/publication/233987484_Fuel_cell_electric_vehicles_and_hydrogen_infrastructure_Status_2012/figures?lo=1 Fig. 8 Fuel cell stack efficiency (dotted lines) and fuel cell system efficiency (straight line) over net power; HydroGen4 standard fleet version: blue curves; ‘‘TechDemo’’ system: green curves U. Eberle et al., Fuel cell electric vehicles and hydrogen infrastructure: Status 2012 Energy & Environmental Science 5(10: 8790 (2012)

17. Conclusions (from all five lessons) • Teachers are ready to add activities to curricula • Introducing notions on environment, energy, climate are useful • Some simple, chosen experiments on electricity, electrochemistry, hydrogen and energy could be done • Additional support material is still welcome • Narration and experiments can be easily adapted to different levels of schools NCU Group: A. Karbowski, K. Wyborska, K. Fedus, K. Rochowicz, A. Kamińska, G. Karwasz