If a fan moves the air and thus adds energy to the room, shouldn't the temperature go up, not down?

  • $\begingroup$ It doesn't cool the room. It causes air to flow past your skin and enhances the rate of heat transfer between your skin and the room air as well as causing cooling by evaporation of moisture from your skin. $\endgroup$ – Chet Miller May 13 at 10:45

Of course the fan does the mechanical (rotational) work on the air thus increases the internal energy of air in the room which results in rise of temperature of the room. But one should know that moving air removes the heat energy from out skin by convection which makes one feel colder but actually the room temperature increases with the time as fan does work on the room air according to first law of thermodynamics $$Q=\Delta U+W$$
Assuming no heat loss from the room i.e. $Q=0$, $$0=\Delta +W$$ $$\Delta U=-W$$ The work done $W$ by the fan on the air is negative thus $\Delta U=-W$ will be positive i.e. the fan increases internal energy of the air molecules in the room which causes rise in temperature.

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