ENERGY

  1. Work and Heat.
    1. Julius Robert Mayer (1814-1889), a German physician, in 1842, in a long essay, entitled Remarks on the energies of inorganic nature, stated the connection between mechanical energy, potential and kinetic, and heat. He concludes,
      "If potential energy and kinetic energy are equivalent to heat, heat must also naturally be equivalent to kinetic energy and potential energy.... [Consequently] we will close our disquisition from the principle causa aequat effectum [the cause is adequate to the effect] and which are in accordance with all the phenomena of nature, with a practical deduction... How great is the quantity of heat corresponds to a given quantity of kinetic and potential energy?"
      Up to this point in his essay Mayer's presentation has been almost completely qualitative, and indeed was reminiscent of Scholastic philosophy of the Medieval Period. This is understandable, since Mayer himself had then no facilities for experimentation and the physicists of his time were quite uncooperative. But here, at the end of his essay, he proposes a quantitative test of his theoretical argument. Here is a chance for empirical verification. And the type of experiment that Mayer choose to be considered was the only one available at the time upon which the determination of the mechanical equivalence of heat could be based.
    2. The experiment. Consider the following experiment: A sample of gas is enclosed in a cylinder, having one freely moving end or frictionaless piston. When the gas is heated, it expands and pushes the piston outward in such a way that the pressure of the gas remains constant and equal to the outside air pressure. This called an isobaric process. Now the pressure P of the gas on the piston is defined as the ratio of the force F exerted by the gas to the area A of the piston face; that is,
      P = F/A. (1)
      Hence, the force F on the piston of area A under pressure P is
      F = PA. (2)
      The expanding gas that is being heated pushes the freely moving piston out a distance Δs. And the work ΔW done by the pressure of the gas on the piston as it moves is equal to the product of the force F exerted by the pressure of the gas and the distance Δs through which the force moves the piston; that is,
      ΔW = FΔs; (3)
      But by equation (2) the force F is equal to the product of the pressure P of the gas and the area A of the piston under pressure; substituting for F in equation (3), we get
      ΔW = PAΔs. (4)
      Now the product of the area A of the face of the piston and the distance Δs it moves is simply the increase in volume ΔV, that is,
      AΔs = ΔV. (5)
      Substituting into equation (4), we get
      ΔW = PΔV; (6)
      That is, the work done by the pressure of an expanding gas is equal to the product of pressure P of the gas and the change of volume ΔV. Since the pressure of the gas is equal the normal atmospheric pressure of 1.013 × 105 nt/m2, and the change in volume per kgm of the enclosed air for each degree centigrade rise in temperature, is known by experiment to be
      2.83 × 10-3 m3/kgm,
      then the work done per kgm of enclosed air is
      ΔW = PΔV = (1.013 × 105 nt/m2)(2.83 × 10-3 m3/kgm)
      ΔW = 287 nt-m/kgm = 287 joules/kgm.

  2. Mechanical Equivalence of Heat.
    1. Definition of Mechanical Equivalence of Heat: For any quantity of work done or mechanical energy expended to produce heat, there exists an exact equivalent quantity of heat. That is,
      W = JQ, (7)
      where W is the work done and Q is the quantity of heat produced. The quantity J is called Joule's constant or the mechanical equivalence of heat and is the ratio of the work done to the heat produced; that is,
      J = W/Q. (8)
      The equation (7) is sometimes called Joule's Law: the work done is directly proportional to the heat produced, where J is the constant of proportionality.
    2. History of the Mechanical Equivalence of Heat.
      (1) Benjamin Thompson (1753-1814), better known as Count Rumford of Bavaria, in 1789, suggested this mechanical equivalence of heat, but he did not measure it. He apparently was content with showing that the quantity of heat produced in friction experiments (boring of canons) could be very large and the source of the heat thus generated was apparently inexhaustible.
      (2) James Prescott Joule (1818-1889), a British amateur scientist, son of a well-to-do brewer, whose business he inherited, attempted to measure the mechanical equivalence of heat constant J. His motivation was religious - he said that it was "manifestly absurd to suppose that the powers with which God had endowed matter could be destroyed", and personally - he loved to experiment, and practically - he wanted to find a cheaper motive power for his brewery.
      (a) In 1843, Joule announced his first results to determine the value of the mechanical equivalence of heat constant, that is, the ratio of the work needed to operate an electric generator to the heat produced by the electric current thus generated. The value he obtained was 4510 joules/kcal.
      (b) Later the same year, 1843, he measured the ratio of the mechanical work needed to maintain the flow of water through thin pipes to the heat of friction produced by the flow. The value he obtained this time was 4140 joules/kcal.
      (c) In the next year, 1844, he measured the ratio of work needed to compress a gas to the heat produced. The value he obtained this time was 4270 joules/kcal.
      (d) In 1847, he reported at a scientific meeting his experiments in which water or sperm oil in a heat-insulated container (a calorimeter) was stirred by a paddle wheel. The ratio of the work done to the heat of friction is 4200 joules/kcal. William Thomson (later Lord Kelvin) at this meeting pointed up the significance of Joule's work.
      (e) In 1848, he reported his experiments involving friction in water and in mercury and the friction of two iron disks rubbing together.
      (f) In 1850, he summarized all his previous work and assigned a value of 4150 joules/kcal to the mechanical equivalence of heat.

      Joules' Law - Modern System of Units and Values
      Quantities British, FPS CGS MKS Hybrid
      W = work done foot-pounds ergs joules joules
      Q = heat produced BTU calories, cal kcal calories, cal
      J = Joule's constant 778.86
      ft-lb/BTU       		4.18605 × 107 ergs/cal 4.18605 × 103 joules/kcal 4.18605
      joules/cal

  3. The Law of Conservation of Energy (LCE).
    1. The Statement of the LCE: Energy is indestructible and interconvertible; energy can neither be created nor destroyed. For a closed or isolated physical system, the sum of all forms of energy remains constant or the net changes add up to zero. The law has been generalized into a universal law: the total amount of energy in the universe is constant.
    2. The History of the LCE.
      (1) Joule in 1803 assumed "that the grand agents of nature are, by the Creator's fiat, indestructible; and that wherever mechanical force [energy] is expended, an exact equivalent of heat is always obtained."
      (2) Julius Robert Mayer (1814-1889), a German physician, in 1842, presented the LCE in a long essay entitled Remarks on the energies of inorganic nature. He states: "Taking both properties together, we may say, causes [energies] are quantitatively indestructible and qualitatively convertible entities... Energies are therefore indestructible, convertible entities." This presentation was almost completely qualitative, using many philosophical arguments. Mayer's idea was not recognized for about 20 years.
      (3) Hermann von Helmholtz (1821-1894), a German physiologist and physicist, in 1847 at the age of 26, extended the energy conservation principle to include all life processes as well as those of physics and chemistry. He did what Mayer had not quite done and what Joule had not attempted. That is, he showed by mathematical demonstration the precise intent of the validity of the conservation principle in various other fields (mechanics, heat, electricity, magnetism, physical chemistry, and astronomy). And with its aid he was able to derived explanations for old puzzles as well as to predict new and confirmable quantitative relations.

    3. The Importance of LCE.
      "The principle of the conservation of energy provided striking general connections among the sciences. It was perhaps the greatest step toward unity in science since Newtonian mechanics, and it was a powerful guide in the exploration of new fields. For this reason, and also because of its practical value, the principle may be regarded as one of the greatest achievements of the human mind."
      [See Gerald Holton and Duane H. D. Roller,
      Foundations of Modern Physical Science, p. 351.]
    4. Conservation Principles in Physics.
      There are four conservation principles in Physics.
      (1) Conservation of Mass.
      (2) Conservation of Momentum:
      (a) Conservation of linear momentum, and
      (b) Conservation of angular momentum.
      (3) Conservation of Energy:
      (a) Conservation of mechanical energy,
      (b) Conservation of heat energy, and
      (c) The law of mechanical equivalence of heat.
      (4) Conservation of Electrical Charge.
  4. The Laws of Thermodynamics.
    The science of thermodynamics has as its concern the tranformation of heat energy into mechanical energy. Thus theromdynamics plays an important in technology, since all sources of "raw" energy available is liberated in the form of heat energy and as such is converted into mechanical energy by some device. At first the sources of raw energy was coal and petroleum but the recent innovation of the nuclear reactor involves the conversion of nuclear energy into heat energy, and its utilization poses problems almost identical to those that arise in the utilization of heat from the earlier sources. A device that converts heat energy into mechanical energy is called heat engine, and the principles that govern its operation are the same whether its input heat ultimately originates in the fisson of uranium nuclei or in the oxidation of hydrocarbon molecules.
    1. The First Law of Thermodynamics.
      All transformations between heat and mechanical energy occur in some type of "system." A particlar system may be a gasoline engine, a human being, or the earth, but in every case three kinds of thermodynamic processes occur. These characteristic processes are:
      (1) the transfer of heat (Q) to or from an external source,
      (2) the storage of energy (U),
      (3) the performance of work (W),
      either by the system on its surroundings, or
      by the surrounding on the system.
      Different systems carry out these processes in different ways, but the principle of the conservation of energy holds in every case. This fact of energy conservation is called the first law of thermodynamics.
      Energy cannot be created or destroyed,
      but may be converted from one form to another      .
      A convenient way of expressing the first law of thermodynamics in its application to a system that undergoes the above three kinds of characteristic processes is:
      ΔQ = ΔU + ΔW. (9)
      In this equation the ΔQ is the heated added to the system; if the system gives off heat, ΔQ is negative. The quantity ΔU is the change of the system's internal energy content U. When U increases, ΔU is considered positive; and when U decreases, ΔU is considered negative. The work done by the system on the outside world is ΔW, so ΔW is negative if work is done by an external agency on the system. In the case of a heat engine operating in a cycle that is continuously repeated, energy may be alternately stored and released from storage, but during a complete cycle the work performed by such an engine cannot exceed the amount of energy supplied to it in that cycle. The work output of the engine is equal its net heat input, that is, the amount of heat it takes in from a reservoir at high-temperature Qh minus the amount of heat it exhausts to a reservoir at low-temperature Qc, that is,
      W = Qh - Qc, (10)
      In a gasoline engine the high-temperature reservoir is the exploding mixture of air and gasoline in the cylinders of the engine and the low-temperature reservoir is the exhaust gas; in the atmosphere of the earth the ultimate high-temperature reservoir is the sun and ultimately the low-temperature reservoir is the rest of the universe.
    2. The Second Law of Thermodynamics.
      The second law of thermodynamics is the physical principle, independent of the first law and not derivable from it, that supplements the first law by limiting the choice of heat sources for the heat engine. It can be stated in number of different ways; a common one is the following:
      It is impossible to construct an engine, operating in cycles (that is, continuously) which does nothing other than take heat from a source and perform a equivalent amount of work.
      According to this law, then no engine can be completely efficient; some of its heat input must be ejected. The thermal efficience, e, of a heat engine is defined as the ratio of the work done to the heat absorbed during one cycle, that is,
      e = W/Qh = (Qh - Qc)/Qh = 1 - Qc/Qh, (11)
      Efficiency may be thought of as the ratio of "what you get" (mechanical work output) to "what you pay for" (energy input). This equation shows that a heat engine is 100% efficient (e = 1) only if Qc = 0, that is, if no heat is expelled to the cold reservoir. But that is not possible and that is what the second law says.

      It can be shown that the greater the efficiency of any heat engine is capable of depends upon the temperature of its heat source (Th) and of the temperature of its heat sink (Tc), the reservoir to which it exhausts heat. That is,
      e = 1 - Tc/Th, (12)
      The greater the difference between these temperature, the more efficient the engine. The second law is the consequence of this fact.

      The direction of heat flow is from a reservoir at a high-temperature to a reservoir of heat at a low-temperature, regardless of the total heat content of each reservoir.
      This second statement may be considered as an alternate statement of the second law of thermodynamics.

      This means that if we are to utilize the heat content of the atmosphere or of the oceans, we must first provide a reservoir at a lower temperature than theirs in order to extract heat from them. There is no reservoir in nature suitable for this purpose, for if there were, heat would flow into it until its temperature would reached that of its surroundings. To establish a low-temperature reservoir, a refrigator must be used, which is a heat engine running in reverse by using up energy to extract heat, and in so doing it will perform more work than that which can be successfully obtained from the heat of atmosphere or oceans.

      The second law of thermodynamics determines the maximum fraction of the energy absorbed by an engine as heat that can be converted to mechanical work. The basis of this law lies in the difference between of the nature of internal energy and of mechanical energy. The former is the energy of random molecular motion, while the latter represented ordered energy. Superposed on their random motion, the molecules of a moving body have have an ordered motion in the direction of the velocity of the body. This is what is called, in mechanics, kinetic energy of the body. The kinetic energy associated with the random motion of the molecules constitute the internal energy. When the moving body makes an inelastic collision and comes to rest, the ordered portion of the molecular kinetic energy becomes converted into random motion. Since it is impossible to control the motion of individual molecules, it is impossible to convert random motion again completely to ordered motion. But a portion can be converted and that is what is accomplished by a heat engine. All these matters and spontaneous thermal processes can be treated quantitatively in terms of a concept called entropy. Entropy, denoted by S, is a measure of the randomness or disordered in a system. The more disorder the greater the entropy. If the disorder in a system increases, then the entrophy of the system increases. The increase of entropy corresponds with the increase of disorder among the molecules that make up a physical body. Rudolph Clausius (1822-1888), who introduced the the concept, stated the second law of thermodynamics in terms of it:
      The entropy of the world tends to a maximum.
      The second law is usually stated in terms of entropy of a closed system:
      The entropy of a closed system increases to a maximum.
      And this can be generalized to the whole universe, since it is a closed system. This means that the total amount of disorder in the universe is increasing.

    We can summarize the laws of thermodynamics by saying that the first law prohibits the work output of heat engine exceeding its heat input, and the second law prohibits the engine from doing that well.