![]() ![]() To visualize one such infinitesimal heat cycle-say, the first one-we have prepared the two bodies in initial states using reservoirs at temperatures T 1 and T 2. The envisaged reversible step requires the presence of a heat engine, a reversible work source, and a set of auxiliary heat reservoirs. We argue below that T F > T f holds not only for the case with algebraic means but also in general. Therefore, we can say that the condition T F > T f directly implies Δ S > 0. (3) may be reexpressed as Δ S = ( C 1 + C 2 ) ln ( T F / T f ). ![]() 14 Now, T f is determined by the reversibility condition: C 1 ln ( T f / T 1 ) + C 2 ln ( T f / T 2 ) = 0, yielding T f = T 1 α T 2 1 − α. 1,12,13 This may be achieved by introducing a heat engine and running infinitesimal, reversible heat cycles that gradually reduce the temperature difference between the two bodies, until the two bodies obtain a common temperature T f. More precisely, consider a reversible process that extracts work from the two bodies initially at temperatures T 1 and T 2. 2–11 However, the fact that one of the means in the above comparison, T 1 α T 2 1 − α, is also the final common temperature of the two bodies when subjected to the process of reversible work extraction, seems to have escaped attention in the literature so far. There has been previous discussion around this apparent correspondence between physical laws and mathematical facts such as these inequalities. Thus, the released heat energy and other metabolic by-products have increased the entropy within the food web.In this case, the proof of the inequality Δ S > 0 rests on the inequality between weighted arithmetic and geometric means, given by α T 1 + ( 1 − α ) T 2 > T 1 α T 2 1 − α, for T 1 ≠ T 2. Carnivores harvest the chemical energy produced by herbivores-with only a fraction of it representing the original radiant energy from the sun-and also release heat energy with carbon dioxide into their surroundings. When primary consumers, like herbivores harvest chemical energy from plants, they also release a small amount of heat energy along with carbon dioxide during metabolism. When primary producers, such as plants, receive energy from the sun and make food, a small amount is transformed into unusable heat energy and is released along with oxygen into the environment. Similar to the First Law of Thermodynamics, the Second Law of Thermodynamics can also be demonstrated within a classic food web. As such, the more energy that a system loses to its surroundings, the less ordered and the more random it becomes. This heat energy can temporarily increase the speed of molecules it encounters. In every energy transfer, a certain amount of energy is lost in a form that is unusable-usually in the form of heat. The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. As a result, the heat energy and other metabolic by-products released at each stage of the food web have increased its entropy. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. This can also be demonstrated in a classic food web. Each energy transfer results in a certain amount of energy that is lost-usually in the form of heat-that increases the disorder of the surroundings. ![]()
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