Truth that Contacting of Different Qualities Releases Energy (5)

In thermodynamics textbooks, the Carnot cycle is used as a model of a heat engine to explain how work energy is extracted through heat transfer. However, I didn’t even understand what I didn’t understand. I didn’t know what the model was trying to convey.
Now I can say this: the Carnot heat engine represents the extraction of energy through reversible heat transfer. Reading the equations repeatedly made them stick in my memory, giving me the illusion of understanding. But after some time, the clarity would fade again—because I hadn’t yet arrived at the concept of reversibility.
In my previous explanation, I connected the term “entropy,” introduced at the end, with reversible heat transfer. Still, it probably doesn’t feel completely clear yet. I’d like to explain the concept of entropy a bit more intuitively.
Thermal energy is expressed as the product of temperature and entropy. This expression lies at the heart of thermodynamics. It‘s a simple formula, so it’s easy to remember and gives a sense of understanding.
Even in junior high school science, thermal energy was expressed as the product of heat capacity and temperature change. The formula shares the same form with the one involving temperature and entropy, making the two intuitively relatable.
In junior high, the case of constant heat capacity with changing temperature was studied. In thermodynamics, an additional component is added—something that changes the quantity or number of states that carry heat.
What carries heat is no longer heat capacity, but the term “entropy.” Imagine inflating a balloon at constant temperature and pressure. As volume increases, internal energy increases. This illustrates the idea of reversible increasing entropy while keeping temperature constant.
Appendix 3 helps deepen intuitive understanding of entropy.

It is assumed that thermal energy Q can be expressed as the product of temperature T and the change in entropy δS. Since this is fundamental, some people may accept it without further explanation.
We learned the following ideal gas law in high school.

PV=nRT (R is the gas constant, n is the number of moles, P is pressure, and V is volume)

Both the left and right sides of this equation correspond to the energy of the gas. (Strictly speaking, 3/2 nRT represents the internal energy (thermal energy), but here the factor 3/2 is ignored here.)
Comparing the assumed thermal energy Q = TδS with the ideal gas law, δS is analogous to nR. An increase in δS is equivalent to an increase in n (the amount of gas or the number of molecules).
At constant pressure, this corresponds to an increase in volume. This concept is illustrated in Figure 2-3.

[ Author : Y. F. ]