Chapter 11: The Invisible Ledger — The Birth of the First Law of Thermodynamics

Continuation of this

The pulsation of the 'iron giant' pumping water from the depths of the earth posed an overwhelmingly massive question to the primitive man's workshop. The primitive man had once deciphered Newton's 'Principia,' which had drifted from the continent, and had established the foundations of mechanics, but he had not yet reached a point where he could fully explain the behavior of this heat-producing machine.

1. The Paradox of the Cycle

The primitive man was intently observing the behavior of the gas reciprocating inside the cylinder.

Heating and expansion: Steam pushes the piston up, lifting heavy groundwater. This means the gas performed 'work' on the outside and consumed energy.

Cooling and contraction: The gas shrinks due to cold water, and the piston returns to its original position. This is the opposite phenomenon to expansion and can be interpreted as proof that the gas has lost energy.

'The gas returns to its original state and prepares for the next task. For this cycle to hold true, the energy balance combining heating, expansion, cooling, and contraction must be zero.'

However, although 'Principia' contained descriptions of momentum and force, the modern concepts of 'work' and the conservation of 'energy' had not yet appeared in a clear form. Even with the primitive man's exceptional intelligence, he had not been able to take the final step to prove the strict equivalence of this invisible 'heat' and 'work'.

2. The Awakening of the Disciple — The Resurrected Memory of Mechanics

At that moment, the fifteen-year-old disciple who had been recording the numerical values on the side was suddenly seized by a violent tremor. He was a foreign child who had drifted ashore long ago, clutching 'Principia' from a collapsed continent. Deep within his consciousness, the words of more refined masters of mechanics like Euler and Lagrange, which he had heard in his homeland, were etched as fragments of old memories.

The disciple roared! 'That is it! Master, I, I have just seen the truth of the world!'

In his eyes, it was no longer just an iron machine, but a torrent of energy flowing through the universe.

'Heat is not a ghost that vanishes! It is the one and only currency circulating through the universe! The heat Q that you, Master, poured in from the boiler. And the work W that the gas performed by pushing out the surroundings and moving the pump. The difference is the very increase or decrease in the energy ΔU hidden inside the gas! If the gas completes a cycle and returns to its original state, the increase or decrease in its internal energy must necessarily be zero! Therefore, the sum of the heat poured in during the cycle and the sum of the work released by the machine to the outside must match without the slightest discrepancy!'

Grabbing a stone tablet with trembling hands, he carved an incredibly beautiful 'ledger of the universe' that integrated the mechanics and thermodynamics known until then.

ΔU=Q−W

'Look! If you subtract the work done from the heat poured in, you derive the change in internal energy, which is the balance! Nothing is wasted, nothing vanishes into nothingness! The universe maintains its dignity through this 'conservation' known as perfect equivalent exchange!'

Illuminated by the light of the blazing furnace, the disciple's shout shattered the silence of the workshop. The visible 'work' and the invisible 'heat.' The two were now firmly bound together under the concept of 'energy'.

3. Establishment of the First Law of Thermodynamics

The primitive man looked at the formula the disciple had carved, quietly and deeply. It was the moment when the unit of heat '1 cal' that he himself had defined and the unit of work in mechanics were completely translated by a single universal law.

'...You win. You expressed in a formula what I could not put into words even when I tried. I finally understand what I wanted to say. It means that when the sum of Q and W is equal during the cycle process, the device returns to its original state. In other words, ΔU=0.'

Thus, the first law of thermodynamics—the law of conservation of energy—was declared in the primitive workshop by the hand of a disciple who harbored the knowledge of the future in his subconscious.

To be continued

Practice Problem

Problem: When 1000 J of heat is added to the gas in a cylinder and the gas performs 400 J of work on the outside, what is the amount of change in the internal energy of the gas?

Answer: From the first law of thermodynamics ΔU=Q−W,

ΔU=1000 J−400 J
ΔU=600 J
Therefore, the internal energy increases by 600 J.