Yes, a hot cup of coffee will eventually freeze if you put it in a freezer, although it may take some time depending on the temperature of the coffee and the freezer.
When you place a hot cup of coffee in a freezer, the heat energy from the coffee will start to transfer to the surrounding air and objects in the freezer. As the heat dissipates, the temperature of the coffee will gradually decrease.
Once the temperature of the coffee drops below the freezing point of water, which is 0 degrees Celsius or 32 degrees Fahrenheit, the liquid water in the coffee will begin to solidify and form ice crystals. The time it takes for the coffee to freeze will depend on various factors, such as the initial temperature of the coffee, the size and shape of the container, and the temperature of the freezer.
It's worth noting that hot liquids can sometimes undergo a phenomenon called "supercooling," where they remain in a liquid state below their freezing point due to the lack of nucleation sites for ice crystal formation. However, if you disturb the supercooled coffee or introduce a foreign object, it can trigger rapid freezing.
In summary, while a hot cup of coffee will eventually freeze in a freezer, the exact time it takes for freezing to occur can vary depending on several factors.