How did the laws of thermodynamics and the concept of entropy develop in the 19th century from the 18th century caloric theory?

The concept of heat from the caloric theory of the 18th century evolved into the equivalence of work and heat and the law of conservation of energy through Joule’s experiments in the 19th century, which were established by Clausius as the second law of thermodynamics and the concept of entropy.

 

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In the 18th century, it was accepted that the substance of heat was caloric, and that caloric was a collection of massless particles that had the property of flowing from higher to lower temperatures. This is called the caloric theory, which states that when a cold object and a hot object are placed in contact, the temperature of the two objects becomes the same because calories move from the hot object to the cold object. One of the big concerns for scientists in this situation was the thermal efficiency of heat engines, such as steam engines.
A heat engine is an organ that does work by absorbing heat from a high-temperature heat source and releasing heat to a lower-temperature source outside the heat engine, such as the atmosphere, and thermal efficiency is defined as the amount of work done by the heat engine relative to the amount of heat absorbed. In the early 19th century, Carnot addressed the problem of thermal efficiency of heat engines based on caloric theory. Carnot noted that when water flows from high to low to do work in a hydraulic engine such as a waterwheel, the ratio of the amount of water to the amount of work done depends only on the height difference. In the same way that water is moved by height differences, calories are moved from high to low temperatures to do work, and the thermal efficiency of a heat engine depends only on these two temperatures.
Meanwhile, attempts to increase the thermal efficiency of these heat engines became a critical challenge with the Industrial Revolution. The Industrial Revolution brought rapid technological advances centered on energy conversion and efficiency, which led to a variety of research efforts to improve the efficiency of heat engines. In this context, Carnot’s work laid the foundation for the first and second laws of thermodynamics, which became important reference points for subsequent scientists.
In the 1840s, Joule conducted experiments to measure the amount of energy required to obtain a certain amount of heat. One of these was the work of heat experiment. This experiment was not done with a heat engine, but rather with a dropped pendulum that spun a wing wheel in water. The amount of heat is expressed in calories, and he measured the work of heat, the amount of work required to obtain one kcal of heat, through precise experiments on the transformation of mechanical energy, work, into heat. Joule thus demonstrated that work and heat are interchangeable physical quantities that differ only in form and are therefore equivalent, and he found that the combined energy of heat and work is conserved when they are interconverted. This led to the law of conservation of energy, which states that not only heat and work, but also chemical and electrical energy, are equivalent and that the total amount of energy remains unchanged when they are converted.
This understanding of heat and work led to a reexamination of Carnot’s theory by scientists. In particular, Thompson pointed out that Carnot’s description of the heat engine, based on the caloric theory, violated Joule’s law of conservation of energy. According to Carnot’s theory, a heat engine works by releasing all of the heat it absorbs at a higher temperature to a lower temperature. This violated Joule’s equivalence of heat and work and the law of conservation of energy, so the idea that the substance of heat was calories could no longer be sustained. However, Carnot’s theory of thermal efficiency could be sustained by Clausius’ proof. Starting from the assumption that if Carnot’s theory did not hold, heat could flow from a lower temperature to a higher temperature, he proved Carnot’s theory that the thermal efficiency of a heat engine is only related to its two operating temperatures, when the engine absorbs heat at a higher temperature and releases it at a lower temperature.
Clausius noted that there is an empirical directionality in nature, such that heat only flows from high to low temperatures and not the other way around. He also noted that there is an asymmetry in the direction of conversion, such that, unlike when work is converted to heat, a heat engine cannot convert all of its heat to work, i.e., its thermal efficiency cannot be 100%. This discussion of directionality and asymmetry led to the concept of entropy, a new physical quantity to describe it. In formulating the second law of thermodynamics, Clausius used the concept of entropy to explain the irreversibility of natural phenomena and the limiting conditions of energy transformation.
In this way, thermodynamics became more than just a matter of energy conversion, but an important field of study for understanding the fundamental principles of natural phenomena. These principles are applied across many fields of modern science and engineering and underlie many of the technologies we use.