How can you use a spoon to cool cup of coffee.stirring which invovles doing work would seem heat coffee rather than it?

You're right to point out the seeming paradox! Stirring a cup of coffee *does* do work and, technically, add a tiny bit of heat to the coffee. However, the amount of heat added through stirring is negligible compared to the amount of heat the coffee loses to the surrounding air.

Here's why using a spoon actually helps cool your coffee:

* Increased Surface Area: Stirring increases the surface area of the coffee exposed to the air. This allows for faster heat transfer from the hot coffee to the cooler air.

* Convection: Stirring creates currents within the coffee, bringing hotter coffee from the bottom into contact with the cooler air at the surface. This speeds up the cooling process.

* Evaporation: As the coffee cools, some of the water molecules gain enough energy to escape into the air as vapor. This evaporation process also takes heat away from the coffee.

The Bottom Line:

While stirring does technically add a tiny bit of heat to the coffee, the cooling effect from the increased surface area, convection, and evaporation far outweighs the minimal heating from stirring.