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you might want to consider either installing a Peltier cooler, which is nice and small and could be mounted to the ant-box.
Another cool gadget is a simple expansion cooler, where forced air goes thru a tube to a tube of larger diameter. Vortex . I once used a micro-version which looped the airflow (internally) to pre-cool the incoming air; we achieved ...
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This is too late for your homework assignment, but for what it's worth, I got the exact same answers as you listed in your post for each process. Not sure where the book solution comes from.
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