Getting a Glimpse of the Power of the System

After ten minutes, the jeep finally arrived at the university where Michael was currently attending, the Technological Institute of the Philippines. It's a go-to school for those students who want to pursue higher education in engineering. It has an accreditation from several prestigious international engineering organizations, making it a beacon of excellence in the field.

Michael crossed the pedestrian crossing guided by the guard who controlled the traffic. Once crossed, he got in line where guards frisked and checked their ID's bags of each student for security purposes. Michael patiently waited his turn, his mind still swirling with thoughts about the Technological System. When it was finally his turn, he placed his bag on the table for inspection. The guard gave it a quick look-over, then nodded for him to pass.

Michael walked towards the examination room, which is at building nine, second floor, room thirteen. The first subject he'll take his midterms is Thermodynamics.

According to the seniors, thermodynamics is a difficult subject, more difficult than its prerequisites, thermodynamics 2. It was notorious for being a subject where many students struggled, often resulting in lower grades or the dreaded need to retake the course.

Michael ascended the stairs to the second floor, his footsteps echoing in the quiet corridor. As he approached room thirteen, he could feel the tension in the air, almost palpable. The door was slightly ajar, and he could see his classmates inside, some poring over their notes in a last-minute attempt to absorb information, others simply staring blankly ahead, resigned to their fate.

He entered the room and found a spot near the window. The natural light offered some comfort in the otherwise tense atmosphere. Michael pulled out his notebook, flipping through the pages of formulas and notes he had taken during lectures. 

"I can't understand a thing," Michael mumbled. During thermodynamics class, he would often feel sleepy due to the lack of sleep and the complicated concepts discussed. 

As time flew by, more and more of his classmates entered the classroom. His friend, Psylemon, sat next to him. 

"Yow, are you ready?" Psylemon nudged Michael in the arm, pausing as he noticed something off about his friend's face.

Michael forced a half-hearted grin, touching the swollen area gently. "Do I look ready? Besides these formulas looking like hieroglyphs, I'm still dealing with this," he said, indicating his bruised face.

Psylemon's eyes widened with concern. "Man, what happened to you? You look like you went a few rounds in a boxing ring."

Michael sighed, leaning back in his chair and rubbing his temples. "Got mugged last night. Just another chapter in my wonderful life," he said, the frustration evident in his voice.

"That's rough, dude," Psylemon sympathized, his tone turning serious. "You're juggling so much, and now this. Life's really throwing everything at you."

Michael gave a wry smile. "Yeah, studying, working, and now dodging punches. It's just a relentless cycle."

"And the pressure to pass doesn't help," Psylemon added, shaking his head. "It's like we're constantly being tested, not just in exams but in life too."

Michael met Psylemon's gaze, seeing the genuine concern in his eyes. "It's tough, but what can we do? We've got to keep moving forward, right? Maybe things will look up eventually."

Psylemon chuckled softly. "Yeah, keep moving forward."

As they continued to chat, Michael felt a bit of his anxiety ease. Sharing his worries with Psylemon made the burden feel a little lighter. They might not have all the answers, but at least they were in this together.

Just as Michael and Psylemon were trying to lighten the mood, their professor, Mr. Delgado, entered the room. Known among students for his strict demeanor and challenging exams, Mr. Delgado was not particularly well-liked. He had a reputation for setting difficult questions, often leading to a high failure rate in his classes.

"Alright, everyone, please arrange your seats. One seat apart," Mr. Delgado announced in a stern voice as he walked to the front of the class. The chatter in the room immediately ceased, and the students hurriedly rearranged their seating as instructed.

Once everyone was seated, Mr. Delgado began to outline the rules for the exam. "Remember, no looking at your classmate's paper. If I catch anyone cheating, I will not hesitate to tear up your paper right in front of you." His gaze swept across the room, and several students shifted uncomfortably in their seats.

He paused for a moment, his eyes lingering on Michael and Psylemon. "And for those who failed the prelims, this is your chance to make a comeback. Don't waste it." 

"Why is he looking at us when he is saying that?" Psylemon whispered.

"Probably because we failed in prelim."

"But almost everyone failed in prelim," Psylemon responded, a hint of annoyance in his voice.

"Yeah, but you know how he is," Michael replied, trying to keep his voice low. "He likes to put extra pressure on those he thinks aren't doing well."

The professor continued with his instructions. "Time limit is one hour, and two questions only. I should only see a scientific calculator and two piece bond paper on your desk. Anything extra will constitute cheating and will get your midterms exam zero." 

"Two questions?!" Michael screams internally. 

Now, don't get your hopes up when a professor said that the exam contained only two questions within that time limit. Because most of the time, it's a difficult question that needs one hour to solve.

After the briefing, Mr. Delgado distributed the exam papers and the room fell silent except for the sound of papers being turned and pens scribbling. Michael focused on his exam, trying to block out everything else. He read the first question. 

Consider a closed system containing a gas which behaves ideally. The system undergoes a complex thermodynamic process described by the following stages:

Isothermal Expansion: The gas initially at state A (P1, V1, T1) expands isothermally to state B (P2, V2) where P1 = 3.0 MPa, V1 = 0.025 m³, and T1 = 400 K.

Adiabatic Compression: The gas is then compressed adiabatically to state C (P3, V3, T3), where the volume at state C (V3) is the same as the initial volume at state A (V1).

Isochoric Cooling: Finally, the gas is cooled at constant volume to return to its initial state A.

Given that the gas is monatomic with a specific heat ratio (γ) of 1.67, and R (universal gas constant) = 8.314 J/(mol·K), calculate the following:

a) The final pressure and temperature at state B after isothermal expansion.

b) The work done by the gas during the isothermal expansion.

c) The temperature at state C after adiabatic compression.

d) The heat rejected by the gas during the isochoric cooling to return to its initial state.

Note: Assume the process is carried out reversibly in all stages. For the adiabatic process, use the relation PV^γ = constant, and for the isochoric process, remember that the internal energy change is equal to the heat added or removed.

After reading question one, Michael exclaimed inwardly. What is this? Is this even possible to solve in an hour? The complexity of the problem was overwhelming, and he could feel a sense of panic starting to set in.

He glanced covertly at his classmates, noticing that many of them were also staring at their papers with furrowed brows and expressions of confusion. Even Psylemon, who usually managed to stay calm under pressure, looked utterly baffled.

Then suddenly, something popped up in front of him.

[Would you like to know the answer for this technical question for 50 System Points?]

[Available System Points: 1,000]

[Yes or No?]

It was the same holographic screen he saw when he was meeting that Goddess, Eris.

"Am I the only one seeing this?" Michael asked himself. It's growing brightly and it doesn't seem to disturb or attract the attention of anyone else in the room. 

Michael hesitated for a moment, considering the implications. He looked around once more to make sure no one else could see the holographic screen.

Taking a deep breath, Michael mentally clicked 'Yes.' Instantly, the solution to the problem began to materialize on the holographic screen. Detailed steps, formulas, and calculations were laid out clearly. Michael was amazed at the precision and depth of the explanation. It was as if a highly skilled professor was guiding him through the problem.

The answer was intricate, involving several steps that interconnected isothermal, adiabatic, and isochoric processes. Michael quickly began jotting down the solution on his paper, making sure to write it in his handwriting and to understand each step as he went along. He couldn't just copy the solution; he had to make it look like he had worked it out himself.

As Michael worked through the answer, he noticed that the system was deducting points from his total. He hoped it would be worth the cost. With the first question answered, he glanced at the second one, a sense of confidence growing within him. Maybe, with the help of the system, he could actually pass this exam.

He turned his attention to the second question, ready to tackle it with the newfound assistance. But as he read through it, he realized it was another complex problem, one that would likely require more system points to solve. Michael sighed, wondering if he should use the system again or try to solve it on his own.

The clock was ticking, and with each passing minute, Michael felt the pressure mounting. It was a choice between risking it with the system or relying on his own knowledge, which he wasn't sure was enough. He glanced at Psylemon, who was still struggling with the first question, and then back at his paper, knowing he had to make a decision soon. 

Moments later, Michael decided to use his points again, and then the system simply laid out the solution.

Thirty minutes later, Michael rose to his feet and everyone turned their eyes on him.

"Mr. Reyes? Is there a problem?" Mr. Delgado asked.

"I'm done, sir," Michael said and almost everyone in the classroom gasped as they couldn't believe someone had already finished it.

Delgado's brows furrowed. "Can I see your paper?"

Michael hesitantly handed over his paper, his heart pounding in his chest. He watched closely as Mr. Delgado scanned his answers with a critical eye. He didn't seem to notice the swelling on his face. 

The room was silent, save for the occasional shuffle of papers and the scratching of pens against paper. Michael could feel the eyes of his classmates on him, some with disbelief, others with a hint of envy.

Mr. Delgado hummed and nodded along as he perused the answers. His expression, usually stern, softened slightly, showing a hint of surprise. After a thorough examination, he looked up at Michael, his gaze piercing.

"See me after class. You may leave."