2.1 Mechanical and Gravitational Energy

Mechanical forms of energy can be considered as those that relate to movement and position. The most important type is translation or kinetic energy and it can be calculated from Eq. (3). Kinetic energy can be found in the energy of the wind and ocean waves.

The acceleration, g, due to gravity on any mass, due to m2, is given by


2 ’ r2

and on earth, g has a value of about 9.8 m s-2. (The radius of the earth is about 6.37 x 106m and the mass of the earth is about 6.0 x 1024kg.)

The gravitational potential energy of falling water can be considerable if the flow of water and the fall is large. There are many very large power stations
around the world that utilize hydroelectric power. It is a clean energy source, free of chemical pollutants. Unfortunately, there is a limit to the number of places on earth where large volumes of falling water can be found. Hydroelectric power contributes about 2% of the total amount of energy used in the world (a 1994 figure).

There are other types of mechanical energy forms that are scientifically interesting and important but are not on a scale large enough for exploitation as an energy source. These include vibrational, rotational, and electronic energies. The potential energy of a spring is given by

Evib = 1/2kx2, (10)

where x is the displacement of the spring from its rest position and k is the spring constant. Such energies are important in understanding the bonding that takes place between atoms. These vibrational en­ergies are quantized and the available energies are small and given by

Evib = (v + 1/2)hv v = 0, 1, 2, 3…, (11)

where h is Planck’s constant (6.626 x 10~34 J s) and v is the frequency of the vibration This frequency can be calculated from the spring constant and the masses of the two atoms involved in the bond.

Rotational energy is found in molecules and in planets. The rotational energy of molecules is even smaller than the vibration energy of the bonds between atoms. Rotational energy is also quantized and the energies confined to

Erot = J(J4p1)h J = 0, 1, 2, …, (12)

where I is the moment of inertia about an axis.

Electronic energy is the extra energy an outer electron needs to move to a higher electronic orbit. It is also the energy given out when an excited outer electron moves back to its ground state. This energy is radiant energy and sometimes the emission is in the visible region of the electromagnetic spectrum, and we can see it as a color. When sodium atoms are excited (NaCl in a bunsen-burner flame or electri­cally excited sodium vapor in a street lamp), they emit an intense yellow flame. Electronic energy is quantized, and the energies are related to the fre­quency, v, of the emitted electromagnetic energy by

Eelec = hv. (13)

The energies of translating atoms and molecules are also quantized but the allowed energy levels are so close together that the energies can be considered as a continuum, and the equations of Newtonian physics apply to these particles. The allowed energy levels for a particle of mass, m, in a one-dimensional box of length L is given by


ETRANS = 2 n = ^, 2 ^ •••. (14)


There is another type of mechanical energy that is related to steam engines and to expanding gases or vapors. The work done by a gas or vapor when it expands (with a volume change of DV), against a pressure p, is

w = pDV. (15)

As an example, let us consider the work done by a mole of water at its boiling point, as it turns into a vapor (with a volume change of DV = 30 x 10~3 m3), against atmospheric pressure (101325 Pa). The work done is

w = (101325 x 30 x 10-3)J = 3040 J.

This is the energy that drives steam engines.

To put the other larger mechanical energies into perspective, let us consider the kinetic energy of a moving tennis ball and the potential energy of water about to fall.

The energy of a tennis ball (m = 60 g) hit by Serena Williams, traveling at a velocity of 100 km s-1, has a kinetic energy of

Eke = 1/2mv2 = (1/2 x 0.060 x 1002)J = 300 J.

The potential energy of 1.0 kg of water, about to fall 100m under gravity (g = 9.8ms-2) is

Epe = mgh =(1 x 9.8 x 100)J = 980 J.

Both energies are rather small.

2.2 Chemical Energy

Chemical energy is stored in molecules through the bonds that bind atoms, and some of this energy can be released when chemical reactions take place. In this process, some bonds are broken (involving an input of energy) and some bonds are made (involving a release of energy). The overall effect is either endothermic or exothermic. However, for most reactions, the process is exothermic and energy is released. This release is usually in the form of thermal energy.

The thermal energy associated with a chemical reaction is always measured at constant pressure and is known as the enthalpy of the reaction, DrHy, and relates to conditions of 1 bar pressure (105Pa) and 298.15 K. As an example, let us consider the reaction between hydrogen and oxygen:

2H2(g)+O2 (g)=2H2O(g). (16)

This reaction involves breaking two moles (or molecules) of H-H bonds, one mole (or molecule) of O-O bonds and making four moles of O-H bonds. As the values of the bond energies are known (AHH-h = 436 kJ mol-1, AHO-o = 497 kJ mol-1 and AHo_h = 463 kJ mol-1), it is possible to determine the enthalpy of the reaction, ArHy:

(ArHy) = (-4 x 463 + 497 + 2 x 436)kJ

= —483 kJ (the negative sign implies an exothermic process).

The experimental enthalpy value for the formation of two moles of H2O(g) from two moles of H2(g) and a mole of O2(g) is indeed —483 kJ.

It is important to know that the sum of the bond energies in a molecule do not make up the total energy of the molecule. The bond energies relate only to chemical reactions. The total energy involves all types of energies, including the energy of binding protons to neutrons and inner electrons and so on. The total energy of a molecule is difficult, if not impossible, to determine.

Chemical energy is the most important type of energy on Earth. It accounts for 96% of all energy sources. These include oil (37%), coal (24%), natural gas (21%), and biomass (14%). These are 1994 figures. Chemical energy supplies the energy for all modes of transport, whether it be ships, cars, trucks, buses, or planes, through the combustion of hydrocarbons such as gasoline and diesel. Chemical energy also supplies energy to most of the electricity power stations in the world through the combustion of natural gas (CH4), oil, or coal. Typical combustion reactions are

C8H18 (l) +O2 (g) – CO2 (g)+ H2O (l)


ArHy = -5461 kJ mol-1 (17)


CH4(g) +O2(g)-CO2(g)+H2O(l)


ArHy = -890 kJ mol-1. (18)

These reactions involve a relatively large amount of energy for a small mass of fuel. The gasoline reaction (Eq. 17) produces 47900Jpergram of n-octane and the natural gas reaction (Eq. 18) produces 55600Jpergram of methane. The steam engine, by comparison, produces 169Jpergram of H2O.

Biomass energy refers to the use of plant material as an energy resource. It includes the growing of sugar cane and corn for alcohol production (a viable exercise in Brazil and also in the mid-west United States) and the burning of wood for heat and energy. Much of the energy used in third world countries is of the latter type. Another interesting and useful biomass process is the exploitation of methane gas from landfills. The decomposition of organic materi­al, under anaerobic conditions, produces an equal volume of methane and carbon dioxide gases. The methane gas may be used for heating or to generate electricity. Energy from landfill projects are now commonplace in many countries of the world, notably in the United Kingdom and the United States. The energy is a renewable resource and exploitation does reduce the amount of methane gas (a greenhouse gas, which is 27 times more effective that carbon dioxide) that enters the atmo­sphere.

The energy used by humans for mechanical activities such as running, lifting weights, pulling, and so forth comes from the combustion of food (carbohydrates, fats, etc.) in much the same way as does the energy of an internal combustion engine. Not a very nice thought. The combustion process in the human body is done through a series of complex reactions, and the overall reaction looks similar to that of burning wood or diesel! Typical carbohydrate and fat reactions are

C6H12O6(s) +6O2(g) -6CO2(g)+ 6H2O(l)


ArHy = -2803 kJ mol-1 (19)


C45H86O6(s) +63iO2(g) -45CO2(g) + 43H2O(l),


ArHy = -27820 kJ mol-1. (20)

The carbohydrate (glucose) and the fat produce

15.6 kJg-1 and 38.5 kJg-1, respectively. The fat produces more than twice the energy per gram that does the carbohydrate. You might have seen these energy values in health food literature as 3.7 and

9.2 kcal per gram, respectively. The calorie is an old – fashioned unit for energy and 4.18 J = 1 calorie. You might also have seen these energy values written as

3.7 and 9.2 Calories per gram, respectively. The Calorie is a health food unit for a kilocalorie.

Chemical energy is measured in calorimeters and the simplest type is known as a “bomb’’ calorimeter. The bomb is made of thick steel, and is of the order of 100 mm high with an internal volume of about 300 cm3. The only type of reactions that can be investigated in these calorimeters are combustion reactions. The inside of the bomb contains a sample holder and contacts to attach a high-resistance fuse wire. The contacts are connected to a cable through gas-tight seals, to a battery and a switch, outside the bomb. The bomb is also fitted with an oxygen inlet pipe and a pressure valve, rated at 30 atmosphere. The sample (e. g., a few grams of glucose) is weighed out (m1) and placed in the sample holder, and the fuse wire is connected to the contacts and bent so that it passes through the sample. Oxygen is pumped into the bomb until the pressure is about 20 atmospheres. The bomb is then placed in a tank of water, which has been weighed (about 3 kg) (m2) and a thermometer and stirrer placed in the tank. Once the bomb and water has reached equilibrium (30 minutes), the temperature of the water is noted (T1), the fuse is fired through the external switch and battery, and the combustion reaction (Eq. 19) takes place. The heat of combustion heats the bomb, which in turn warms the water. When an equilibrium has been reached (another 30 minutes), the temperature of the water is noted (T2). The bomb and the water should have the same change of temperature i. e., (T2-T1) = AT.

The energy given out by the glucose sample is balanced by the energy absorbed by the water and the bomb. If the energy per mole of glucose combustion reaction is ArUy, then

[(mg/MM)ArUS] glucose = [m2 s2AT] water + [m1s1AT]bomb;


where mg is the mass of glucose, MM is the molar mass of glucose, s2 is the specific heat of the water (4.18 Jg-1 KT1), and m1 and s1 are the mass and specific heat of the calorimeter. The product (m1s1) is unique for each calorimeter (it is called the bomb’s heat capacity) and can be determined from calibra­tion experiments using a standard substance such as benzoic acid. The value of ArUy is calculated from Eq. (21). This energy refers to a constant volume experiment. The value of ArHy is usually very close to ArUy. The exact value can be calculated from

ArHy = ArUy + AnRT, (22)

where An is the change in the amount of gas in the reaction. For this reaction (see Eq. 19), there are six moles of O2(g) on the reactant side and six moles of CO2(g) on the products side. For this combustion reaction An = 0 and ArHy = ArUy.

There is another type of chemical energy that should be considered and that is the energy of a phase change. By phase change we mean a solid changing to a liquid or a liquid changing to a vapor. A common example is the change of liquid water to steam. This type of energy has been called the latent heat and is due to intermolecular interactions which bind molecules together as a result of the attractions of dipoles and fluctuating dipoles that are created by the electrons wizzing around molecules. The larger the molecule, the more electrons in the molecule and the greater will be this interaction and the greater will be its latent heat or its enthalpy of phase change. For water, the enthalpies of fusion (melting) at 273.15 K and vaporization at 373.15 K are 6.0 and 40.7kJmol~1, respectively. It obviously takes a lot more energy to separate the liquid molecules to form a vapor than it does to separate the molecules in solid water to form a liquid. Much of the energy (coal) used to fire up a steam engine is used to overcome the enthalpy of vaporization of water and create steam from liquid water.

It is possible to store energy using the reversible property of phase equilibria. For example, solar energy can readily be used to melt Glauber salts (Na2SO4.10H2O) because of its low melting tem­perature (306 K). This molten material will revert to a solid when the temperature drops below the melting point (at night) and will release the stored energy, which is the enthalpy of fusion.

2.3 Electrical Energy

Electrical energy is the most useful of energies as it can be readily transported along copper or aluminum cables for long distances. It can also be conveniently switched on and off. Electrical energy is not unlike the gravitational energy of falling water with the electrons moving under a potential difference repla­cing water falling under the influence of gravity.

The electrical energy of electrons moving under a potential difference of V with a current i for a time t is

Ee = Vit. (23)

Electrical energy is readily converted from chemical energy, creating a flow of electrons. Such devices are batteries and one such battery is the Daniel cell. The natural reaction between zinc and a solution of copper sulfate to form zinc sulfate and metallic
copper can be demonstrated by placing a piece of metallic zinc in a solution of copper sulfate where­upon the zinc will begin to dissolve and red metallic copper will be precipitated. The overall reaction can be represented as the displacement of the copper ions from solution as metallic copper by the formation of zinc ions from the zinc in the process of which electrons are transferred from the zinc to the copper ions:

Zn(s) + Cu2+(aq) — Zn2+ (aq) + Cu(s). (24)

This reaction can be made to take place in a more controlled way in an electrochemical cell (the Daniel cell), in which zinc and copper electrodes are each immersed in a solution of its sulfate and are separated by a membrane which allows the diffusion of ions. If an external metallic connection (a piece of wire) is made between copper and the zinc rods, an electric current (electrons) can flow between the two rods; zinc metal will dissolve to form zinc ions and the copper ions will deposit as metal on the copper rod. The completion of the flow of electric charge will be achieved by the movement of zinc ions through the membrane and the movement of copper ions toward the copper rod. This electrochemical cell is a prototype of the many different kinds of battery that are used to power various devices from hearing aids to video cameras and flashlights in daily use.

2.4 Radiation of Electromagnetic Energy

Radiation energy is a unique form of energy. It is characterized by a wave with a wavelength and a frequency:

c = 1v. (25)

where c is the speed of light (3 x 108ms ^. The magnitude of radiant energy is given by

Er = hv. (26)

Radiation energy is emitted from an object in the form of electromagnetic waves, which consist of
electric and magnetic fields whose amplitudes vary with time. These waves propagate out from the object at the speed of light. Familiar examples of electromagnetic radiation include gamma rays, X – rays, ultraviolet waves, visible waves, infrared waves, microwaves, TV waves, and radio waves. The full range of the electromagnetic spectrum spans cosmic rays at the short wavelength and radio waves at the long wavelength end (see Fig. 2). It is the wavelength that categorizes the different types of radiation. Only a small region of the spectrum is visible to the human eye. That part is called the visible spectrum. The radiant energy that causes sunburn and possible cancer is the ultraviolet rays. These are of shorter wavelength (hence greater energy) than the visible rays and the infrared rays. It is the latter that gives us the sensation of warmth. These rays have similar energies to the vibration energies of the molecules in our bodies and hence are readily absorbed.

Подпись: Wavelength/m FIGURE 2 The electromagnetic spectrum.

The main source of electromagnetic radiation on Earth is the sun. This radiation involves only the UV, visible and IR parts of the electromagnetic spectrum. Sunlight is the mainstay and support for all plant and animal life on earth. The total amount of sunlight reaching the earth each day is 3.11 x 1023J. This is an enormous amount of energy and 11 days of sunshine over the whole earth is equivalent to all the fossil fuel (gas, oil, coal) in the earth. However, the earth’s surface is large and the amount of sunshine reaching the earth peaks at about 1.2kWm-2 on the equator at midday. This is really a small amount of energy. A solar energy collector of almost 8 km x 8 km is needed to create a reasonably large electricity generating power station of 1.0GW (assuming a conversion factor of 10%). Even this is unrealistic as it assumes all the solar collecting panels are dust free and clean and that the sun shines brightly 8 hours every day. Solar energy is a dilute form of energy, but it is a renewable and clean energy source and will certainly be an important source in the future as the earth’s fossil fuel resources become exhausted.

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