Equivalence of Work and Energy

An experiment is a question which science poses to Nature, and a measurement is the recording of Nature s answer. 

At the simplest level, we can consider the body as a thermodynamic system absorbing energy from its environment and in turn releasing heat and doing mechanical work. 

When speaking of work, we often mean mechanical work, where something is moved from one place to another. The mechanical work to move this thing is calcnlated as 

FIGU RE 2.4.1 Diagram of positive and negative work. The leg muscles produce a force acting on the stairs, but it is the difference between the stair reaction force and body weight that determines the direction of movement. When the resultant force and direction of movement are the same, there is positive work done by the body. When the resultant force and the direction of movement are in the opposite direction, the body does negative work. 

If positive work results from a force in the direction of the movement, and negative work results from a force opposite to the direction of movement, what of a force applied at right angles to the movement In this case, no work is done no positive work and no negative woik. 

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Gaspard Gustav de Coriolis (1792 — 1843), was a French engineer and matheinaticjan and director of the Ecole Poly technique in Paris. In 1835, Coriolis introduced the notion of work, the equivalence of work and energy, and also a coupling of rotation and vibration. 

In the form that we have stated it, this principle applies to a closed cycle only this is a troublesome condition for its application. The principle of the equivalence of work and heat, in the first form stated, possessed the same inconvenience (Chap. II, Art 21) we transformed it in such a way as to remove this inconvenience, and it is this transformation which introduced into our reasonings the quantity called internal energy. We shall transform the theorem of Carnot and dautius in an analogous manner, and this trans-... 

In 1847 Helmholtz formulated his statement concerning the conservation of energy and the equivalence of work and heat Although energy may be converted from one form to another, it cannot be created or destroyed. As a consequence. 

On the other hand, an ultrafast liquid-jet UPS [33], shown in Fig. 35.2, resolved the bound (vertical binding as an equivalent of work function) energies of 1.6 and 3.3 eV for solvated electrons at the water skin and in the bulk solution, respectively. The bound energy decreases with the number of water molecules, indicating the size-induced strong polarization [34]. 

Credit for the first recognizable statement of the principle of conservation of energy (heat plus work) apparently belongs to J. Robert Mayer (Sidebar 3.2), who published such a statement in 1842. Mayer also obtained a (slightly) improved estimate, approximately 3.56 J cal-1, for the mechanical equivalent of heat. Mayer had actually submitted his first paper on the energy-conservation principle two years earlier, but his treatment of the concepts of force, momentum, work, and energy was so confused that the paper was rejected. By 1842, Mayer had sufficiently straightened out his ideas to win publication,... 

The first law is closely related to the conservation of energy (Section A) and is a consequence of it. The first law implies the equivalence of heat and work as means of transferring energy, but heat is a concept that occurs only when we are considering the properties of systems composed of large numbers of particles. The concept of heat does not occur in the description of single particles. 

Joule The meter-kilogram-second unit of work or energy, equal to the work done by a force of one Newton when its point of application moves through a distance of one meter in the direction of the force equivalent to 107 ergs and one watt-second. 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

This proposition bears the name of the principle of the con-servation of energy. It is quite uimecessary to assign to it a vague metaph3rsic sense or a mysterious origin it is simply a special case of a physical law, the law of the equivalence of heat and work. 

But if we denote by W the kinetic energy of the system in a given state, by U the internal energy in this same state, by the work done by the external forces during the modification considered, the principle of the equivalence of heat and work gives [Chap. II, eq. (4)]... 

Entrojiy and probability. The recognition of the universal applicability of the law of the conservation of energy is partly based on the mechanical conception of heat as motion of the ultimate particles of matter. If heat, energy, and kinetic energy of the molecules are essentially of the same nature, and are differentiated from one another only by the units in which we measure them, the validity of the law of the equivalence of heat and work is explained. At first sight, however, it is not easy to understand why heat cannot be converted completely into work, or, in other words, why the conversion of heat into work is an irreversible process (second law of thermodynamics). In pure mechanics we deal only with perfectly reversible processes. By the principles of mechanics the complete conversion of heat into work should be just as possible as the conversion... 

Tnble 1.5-1 E.%periniems Designed to Prove the Energy Equivalence of Heat and Work... 

Though Sadi Carnot used the caloric theory of heat to reach his conclusions, his later scientific notes reveal his realization that the caloric theory was not supported by experiments. In fact, Camot understood the mechanical equivalence of heat and even estimated the conversion factor to be approximately 3.7 joules per calorie (the more accurate value being 4.18 J/cal) [1-3]. Unfortunately, Sadi Carnot s brother, Hippolyte Camot, who was in possession of Sadi s scientific notes from the time of his death in 1832, did not make them known to the scientific community until 1878 [3]. That was the year in which Joule published his last paper. By then the equivalence between heat and work and the law of conservation of energy were well known through the work of Joule, Helmholtz, Mayer and others. (It was also in 1878 that Gibbs published his famous work On the Equilibrium of Heterogeneous Substances). 

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