Truth that Contacting of Different Qualities Releases Energy (8)

Next, we will calculate the amount of heat energy lost when the two capacitors are connected. Since this part is rather technical, you may skip it if you wish.
As the charge moves from capacitor 1 to capacitor 2, the resistor R produces heat, as shown in Figure 2-8. The total amount of heat generated, is obtained by integrating the heat generation over time.

　Heat generation W＝R＊J²＝4Q²/RC²exp-4t/RC

The heat generation continues until the charge becomes evenly distributed. The total heat L can be estimated as a function of time. By integrating the power　W over time, we obtain:

　L =∫Wdt＝(-RC/4)4Q²/RC²exp(-4t/RC)＋Constant
　　＝ -Q²/Cexp-4t/RC＋Constant

By applying the initial condition that L=0 at t=0, the integration constant is determined to be Q²/C. Thus, the final equation is as follows:

　L(t)=Q²/C(1-exp(-4t/RC)

When t→∞, the total heat energy generated is Q²/C. This corresponds to the loss of energy caused by the mixing of charges. The difference between the initial energy E1+E2, when capacitors C1​ and C2 were separated, and the final energy E12​, after they have been connected, agrees with the total heat energy L(t=∞).

We have calculated the energy released when capacitors with different amounts of charge are connected. When the amount of charge differs, a difference in potential (voltage) arises. When the voltages are different, the charge moves from the higher potential to the lower potential. During this movement, if the path of transfer is a conductor, energy is released as heat corresponding to its resistance. When the resistance is large, the charge moves slowly over a long period of time. When the resistance is small, a large current flows instantaneously.
Here, we have taken as an example the connection (charge transfer) between capacitors with different stored charges. The behavior of charge transfer is very similar to the mixing of water at different temperatures. If we reinterpret the electric charge Q as heat energy Q, and voltage V as temperature T, we obtain the same expression.
When water at a high temperature T1 is mixed with water at a low temperatureT2, heat flows from the high to the low temperature. Through the mixing process, the total heat energy Q originally possessed is not conserved but partially lost. To recall this concept, we will re-express it in terms of heat energy.

　Q1​=CT1​
　Q2​=CT2​
　here
　C: heat capacity

　Q1＋Q2: energy possessed by the water when isolated

After mixing high and low temperatures, the resulting thermal energy Q12 is

　Q12=Q1​+Q2 ​−L

　where
　L: Energy lost due to mixing

I think we can see that the discussion about electricity is quite similar to that about water.
And here, there is another thing we can understand.

Expression of Energy Lost by Mixing is

　Q12=Q1+Q2−L

Let us rearrange this as

　Q12+L=Q1＋Q2

From the original viewpoint, 𝐿　appears to represent a loss. However, it can also be regarded as the energy gained through mixing. In other words, when different substances come into contact and mix, this equation expresses the generation of energy.By utilizing that energy, something new can be achieved.


Social phenomena exhibit analogous patterns.
The qualitative disparity between wealth and poverty remains imperceptible in isolation but becomes discernible through interaction. Such disparities manifest as forms of energy—expressed in ambition, social unrest, or the pursuit of material wealth. Similarly, a nation’s vitality emerges from the aggregated energy of its citizens and is reflected in social indicators such as population and gross domestic product (GDP).
This notion can be elucidated through a thought experiment. Japan’s population is approximately 130 million, yet its GDP has remained virtually stagnant for the past three decades. If every individual were homogeneous in nature, would GDP increase or decrease? If all citizens lived under comparable living conditions, would GDP grow or contract? If everyone were equally happy, would GDP expand? The answer appears self-evident—GDP would most likely decline.
Conversely, if society were composed of heterogeneous individuals, disparities would naturally arise, producing both affluent and impoverished classes. While diversity would give rise to ambition and aspiration, it would also generate social tension and crime. Interactions among homogeneous individuals are unlikely to produce significant energy or dynamism. Thus, the dynamics of social phenomena may be interpreted analogously to the interactions observed in physical systems such as the flow of water or electricity, as previously discussed in this study.

[ Author : Y. F. ]