Heat into Work

Spontaneous and Irreversible Processes.—In order to understand something of the conditions which determine whether a particular process will occur or not, it is of interest to examine certain processes which are known to be spontaneous, that is, processes which take place without external intervention of any kind. The expansion of a gas into an evacuated space, or from any region of higher into one of lower pressure, takes place spontaneously, until the pressure distribution is uniform throughout. Similarly one as will diffuse spontaneously into another until the mixing is complete and the system has e same composition in all parts. Diffusion 

Before stating the second law, other attempts to reverse spontaneous processes will be considered. When a bar of metal, which was originally hotter at one end, has attained a uniform temperature, the initial state 

It is evident that certain spontaneous physical processes could be reversed if the complete conversion of heat into work could be achieved it will now be shown that similar considerations apply to chemical reactions. A piece of zinc, for example, will dissolve spontaneously in an aqueous solution of copper sulfate, according to the equation 

It will be recalled from the statements in 9d that in an isothermal, reversible expansion of an ideal gas the work done is exactly equal to the heat absorbed by the system. In other words, in this process the heat is completely converted into work. However, it is important to observe that this conversion is accompanied by an increase in the volume of the gas, so that the system has undergone a change. If the gas is to be restored to its original volume by reversible compression, work will have to be done on the system, and an equivalent amount of heat will be liberated. The work and heat quantities involved in the process are exactly the same as those concerned in the original expansion. Hence, the net result of the isothermal expansion and compression is that the system is restored to its original state, but there is no net absorption of heat and no work is done. The foregoing is an illustration of the universal experience, that it is not possible to convert 

A consequence of the impossibility of converting heat isothermally into work in a continuous manner is the impracticability of what is called perpetual motion of the second kind/ that is, the utilization of the vast stores of energy in the ocean and in the earth. There is nothing contrary to the first law of thermodynamics in this concept, but the fact that it has not been found feasible provides support for the second law. The ocean, for example, may be regarded as a heat reservoir of constant temperature, and the law states that it is not possible to convert the heat continuously into work without producing changes elsewhere. 

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Carnot s cycle A hypothetical scheme for an ideal heat machine. Shows that the maximum efficiency for the conversion of heat into work depends only on the two temperatures between which the heat engine works, and not at all on the nature of the substance employed. 

Calculate also the activation energy for the reaction, again in kcal/mol, assuming that the Coulomb repulsion maximizes at 3 -y 10 cm separation of the nuclear centers. Assuming a successful cold-fusion device, how many fusions per second would generate one horsepower (1 hp) if the conversion of heat into work were 10% efficient ... 

A heat engine is any arrangement which converts heat into work. 

Heat, like work, is energy in transit and is not a function of the state of a system. Heat and work are interconvertible. A steam engine is an example of a machine designed to convert heat into work.h The turning of a paddle wheel in a tank of water to produce heat from friction represents the reverse process, the conversion of work into heat. 

As we have seen, statements of the laws in terms of the conversion of heat into work in a cyclic engine are equivalent to the statements involving energy and entropy. The conversion from one to the other is not always obvious, but the relationships predicting the efficiency of the conversion of heat into work can be derived from the U and S statements. 

The reversible process (for which the equal sign applies) gives the maximum efficiency for the conversion of heat into work, but even the reversible engine is limited in the extent to which heat can be converted into work. 

This practical problem is of the type that engineers worry about a lot. It demonstrates the difficulty of converting heat into work and the efficiency of actual processes compared with the theoretical efficiency. 

Substitution for K4 jVy from this equation into equation (3.84) and dividing by <72 given by equation (3.79) gives the efficiency 77 of conversion of heat into work for the Carnot cycle as... 

Thus far our examination of the quantum mechanical basis for control of many-body dynamics has proceeded under the assumption that a control field that will generate the goal we wish to achieve (e.g., maximizing the yield of a particular product of a reaction) exists. The task of the analysis is, then, to find that control field. We have not asked if there is a fundamental limit to the extent of control of quantum dynamics that is attainable that is, whether there is an analogue of the limit imposed by the second law of thermodynamics on the extent of transformation of heat into work. Nor have we examined the limitation to achievable control arising from the sensitivity of the structure of the control field to uncertainties in our knowledge of molecular properties or to fluctuations in the control field arising from the source lasers. It is these subjects that we briefly discuss in this section. 

A heat engine is a device for converting heat into work, (e.g., steam engine, internal combustion engine)... 

Landes (20) almost defy compilation and fall under three principles (a) the substitution of machines—rapid, regular, precise, tireless—for human skill and effort (b) the substitution of inanimate for animate source of power, in particular, the invention of engines for converting heat into work, thereby opening an almost unlimited supply of energy and (c) the use of new and far more abundant raw materials, in particular, the substitution of mineral, and eventually artificial materials for vegetable or animal sources. ... 

The Carnot cycle engine achieves what we are looking for, a conversion of heat into work, with return of the engine to its initial state. We note, however, that in order to complete the cycle, we have paid a price. In the isothermal compression at Tc, some of the work produced in the expansion has to be used up to compress the system, finding its way into heat at the cold reservoir temperature. 

Exergetic efficiency r ex for hydrogen production by thermo water-splitting at a temperature Ta can be defined as the quotient of the recoverable work (here equal to the free enthalpy of water formation) divided by this quantity plus the sum of the exergy losses D = Ta AS in the process [Eq. (6)]. Thermal efficiency t T from a heat source at temperature T is linked to this efficiency by transformation of heat into work [Eq. (7)]. 

Silver, R. S., "Considerations Regarding Potential Convertibility of Heat into Work," J. Heat Recovery Syst.. 

It is clear that even at partial transformation of heat into work in open subsystem the maximum entropy of the isolated system will be reached at the largest value of T2. 

Boltzmann [3]. Boltzmann was led to thiB generalized formulation of the problem by some attempts he had undertaken (1866) 11] to derive from kinetic concepts the Camot-Clausius theorem about the limited convertibility of heat into work. In order to carry through such a derivation for an arbitrary thermal system (Boltzmann [5], (1871)) it was necessary to calculate, e.g., for a nonideal gas, bow in an infinitely slow change of the state of the system the added amount of heat is divided between the translational and internal kinetic energy and the various forms of potential energy of the gas molecule. It is just for this that the distribution law introduced above is needed. 

The second law does not prohibit the production of work from heat, but does place a limit oq. the fraction of the heat that may be converted to work i any cyclic process. The partial conversion of heat into work is the basis for nearly all commercial production of power (water power is an exception). The develop ment of a quantitative expression for the efficiency of this conversion is the nex step in the treatment of the second law. 

However, according to statement 1 a of the second law, Q v cannot be directed into the system, for the cycle would then be a process for the complete conversion of heat into work. Thus, j dQnv is negative, and it follows that SA - SB is also negative whence SB > SA. Since the original irreversible process is adiabatic, the total entropy change as a result of this process is AStota, = SB - SA > 0. 

CONVERSION OF HEAT INTO WORK BY POWER CYCLES 2S7... 

Conversion of Heat into Work by Power Cycles 247... 

Scientists also noticed that when they tried to convert heat into work, the matter was not as simple as converting work into heat. A machine, which would take heat and convert into work (a heat engine), would necessarily have to discard some (lower quality) heat (Second Law of Thermodynamics - Sec. 5.1). In other words, difference between heat and work (and other forms of energy) was emphasised by this law. 

It is not possible to convert heat into work by a constant temperature cycle. 

Here heat has been completely converted into work but the system is not in the same state as it was to start with. The system can be brought to its initial state by reversibly compressing the gas to a pressure of P The gas will give out heat to the heat reservoir so that its temperature is maintained at By the time the pressure P, is reached, an equal amount of work, as was performed by the gas during expansion fromP, to P2, will have to be done on it. Consequently, the gas will return an equal amount of heat to the heat source. Hence, after such a system is made to perform in a cycle, the net effect is that no heat is taken up or given out by the system and no work is done by or on the system. This type of experience is compatible with statement (//) of the second law, which says that it is not possible to convert heat into work by a constant temperature cycle. 

Most of the statements of second law pre-suppose the existence of a heat engine or a machine that converts heat into work. From the example cited above, it is clear that if we do conceive of a heat engine it must be working between at least two different temperatures. Before we visualise such a machine, let us assume that such a machine does exist and it can act in cycles in a reversible manner so that we can examine statement (/v) of second law. 

Now the system has reached the original state and the area ABCD represents the net work done by the system, which is not zero. Thus, the system is a heat engine, which has worked in a cycle in a reversible manner and has converted some heat into work. The cycle the system has undergone is called the Carnot s Cycle . 

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