Heat engines, thermodynamic laws

The second law of thermodynamics may be used to show that a cyclic heat power plant (or cyclic heat engine) achieves maximum efficiency by operating on a reversible cycle called the Carnot cycle for a given (maximum) temperature of supply (T ax) and given (minimum) temperature of heat rejection (T jn). Such a Carnot power plant receives all its heat (Qq) at the maximum temperature (i.e. Tq = and rejects all its heat (Q ) at the minimum temperature (i.e. 7 = 7, in) the other processes are reversible and adiabatic and therefore isentropic (see the temperature-entropy diagram of Fig. 1.8). Its thermal efficiency is... 

If all the heat absorbed were converted into work, the efficiency would be 1, or 100 percent. If none of the heat absorbed was converted into work, the efficiency would be 0. The first law of thermodynamics limits the efficiency of any heat engine to 1 but does not prevent an efficiency of 1. The efficiency of practical heat engines is always less than 1. For example, the efficiency of a large steam turbine in an electric power plant is about 0.5, which is considerably more efficient than the typical 0.35 efficiency of an auto engine. When two objects at different temperatures are m... 

This remarkable result shows that the efficiency of a Carnot engine is simply related to the ratio of the two absolute temperatures used in the cycle. In normal applications in a power plant, the cold temperature is around room temperature T = 300 K while the hot temperature in a power plant is around T = fiOO K, and thus has an efficiency of 0.5, or 50 percent. This is approximately the maximum efficiency of a typical power plant. The heated steam in a power plant is used to drive a turbine and some such arrangement is used in most heat engines. A Carnot engine operating between 600 K and 300 K must be inefficient, only approximately 50 percent of the heat being converted to work, or the second law of thermodynamics would be violated. The actual efficiency of heat engines must be lower than the Carnot efficiency because they use different thermodynamic cycles and the processes are not reversible. 

It is commonly expressed that a fuel cell is more efficient than a heat engine because it is not subject to Carnot Cycle limitations, or a fuel cell is more efficient because it is not subject to the second law of thermodynamics. These statements are misleading. A more suitable statement for... 

One hundred fifty years ago, the two classic laws of thermodynamics were formulated independently by Kelvin and by Clausius, essentially by making the Carnot theorem and the Joule-Mayer-Helmholtz principle of conservation of energy concordant with each other. At first the physicists of the middle 1800s focused primarily on heat engines, in part because of the pressing need for efficient sources of power. At that time, chemists, who are rarely at ease with the calculus, shied away from... 

The power output (P) of the heat engine according to the first law of thermodynamics is... 

The second law of thermodynamics requires that gdotn/Tw = fidotL/Tc The efficiency (ly) of the heat engine is i =p/edotH... 

This limitation, imposed by a scientific law called the second law of thermodynamics, can be difficult to understand. It involves a concept known as entropy, which can be thought of as a measure of disorder. Entropy must increase in natural processes in other words, processes naturally go from order to disorder (as observed by anyone who has bought a shiny new bicycle or automobile and watched it fade, corrode, break down, and finally fall apart—usually just after the warranty expires). The second law of thermodynamics requires a heat engine to vent some heat into the environment, thereby raising entropy. This loss is unavoidable, and a heat engine will not operate without it. No one will ever buy a car powered by a gasoline engine that does not exhaust, and lose, some of its heat. 

Heat and temperature were poorly understood prior to Carnot s analysis of heat engines in 1824. The Carnot cycle became the conceptual foundation for the definition of temperature. This led to the somewhat later work of Lord Kelvin, who proposed the Kelvin scale based upon a consideration of the second law of thermodynamics. This leads to a temperature at which all the thermal motion of the atoms stops, By using this as the zero point or absolute zero and another reference point to determine the size of the degrees, a scale can be defined. The Comit e Consultative of the International Committee of Weights and Measures selected 273.16 K as the value lor the triple point for water. This set the ice-point at 273.15 K. 

In the development of the second law and the definition of the entropy function, we use the phenomenological approach as we did for the first law. First, the concept of reversible and irreversible processes is developed. The Carnot cycle is used as an example of a reversible heat engine, and the results obtained from the study of the Carnot cycle are generalized and shown to be the same for all reversible heat engines. The relations obtained permit the definition of a thermodynamic temperature scale. Finally, the entropy function is defined and its properties are discussed. 

The efficiency of reversible heat engines two statements of the second law of thermodynamics... 

Moreover, if is always positive and nonzero, W must be positive and nonzero except in the case when the two temperatures are equal. This observation results in the Clausius statement of the second law of thermodynamics Heat of itself will not flow from a heat reservoir at a lower temperature to one at a higher temperature. It is in no way possible for this to occur without the agency of some system operating as a heat engine in which work is done by the surroundings on the system. 

From the first law (energy conservation) of thermodynamics we have dQi = dW + dQ2, and the second law (entropy creation) of thermodynamics gives us dQx Tx) + dQ2IT2) a 0, where equality is for a reversible heat engine and inequality for an irreversible one. We then have the efficiency dW/dQx) for the reversible heat engine and the efficiency... 

From the discussion of heat engines, the second law of thermodynamics states that it is impossible to achieve heat, taken from a reservoir, and convert it into work without simultaneous delivery of heat from the higher temperature to the lower temperature (Lord Kelvin). It also states that some work should be converted to heat in order to make heat flow from a lower to a higher temperature (Principle of Clausius). These statements acknowledge that the efficiency of heat engines could never be 100% and that heat flow from high temperatures to low temperatures is not totally spontaneous. Simply, the second law states that natural processes occur spontaneously toward the direction in which less available work can be used. 

The second law of thermodynamics can be restated in terms of entropy regardless of heat engines, chemical reactions, or biological transformations of energy in living organisms, as follows ... 

Before attempting to assess the likely future of thermodynamics in chemical engineering, it may be useful briefly to recall the past. In chemical engineering, the primary use of thermodynamics was, and still is, concerned with application of the first law (conservation equations), in particular, with energy balances that constitute an essential cornerstone of our discipline. Another primary use was, and still is, directed at description of fluid behavior, as in nozzles, heat engines, and refrigerators. The fundamentals of these important applications were extensively developed in the first third of this century. 

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