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Ludwig Boltzmann killed himself so that we could do thermodynamics by enumerating the states of a system. Learn to count, the most important skill in statistical mechanics.

In the above circuit, the voltage across the resistor \( R = 13 \ \Omega \) is \( V = 0 \text{ V}. \) If the voltage \( V \) is suddenly increased to \( V' = 13 \text{ V},\) what has happened to the entropy of the system of electrons in the circuit?

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If a warm object contacts a cold object, in which direction will the heat flow?

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If we put a cup of water into a freezer, what will happen to its entropy?

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If ice cream is melted in a warm room, what happens to the entropy of the system?

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