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He picked up his phone and typed back to the group: “Don't use the GDZ. Masha, check your signs on the work equation. The gas is expanding, so the work is positive.”
Ivan put the phone face down. He re-read the paragraph, not as a chore, but as a map. He traced the logic: if the pressure stays the same and the volume grows, the gas must be pushing against the world. It was doing work . Slowly, the abstract symbols began to shift.
Outside his window, the St. Petersburg sky was the color of a bruised plum, but inside, the desk lamp cast a harsh, lonely circle of light over a notebook. He was stuck on a paragraph in the thermodynamics chapter. The words— isobaric processes, internal energy, work done by a gas —felt like a foreign language he was supposed to already know.
An hour later, his notebook was messy with crossed-out calculations, but the final answer sat at the bottom, boxed in ink. He felt a strange, quiet rush—the "Aha!" moment that a GDZ link could never provide.
He closed the Nikolaev book. For the first time all semester, the gatekeeper had let him through.
He sighed, his phone buzzing with a notification from the class group chat. “Did anyone get problem 4? I’ve tried three times and I keep getting a negative Kelvin temperature,” Masha had messaged. “Check the GDZ (Ready Homework Solutions),” someone replied instantly with a link.
Ivan hovered his thumb over the screen. The "GDZ" was a siren song. It was the easy way out—a neat, pre-packaged explanation that would satisfy the teacher tomorrow morning. But as he looked back at the diagram of the piston in his book, a spark of stubbornness flickered.
