Power = work / time = 8000J / 20s = 400W
In my opinion it does. The more water the pot holds, the longer you need to wait for it to freeze. Since there is more water, some parts may not be completely frozen. An experiment you can try is to get an ice cube container and a pot. fill both of them and put them in the freezer for the same amount of time. When you take it out, the ice cubes should be frozen leaving the pot with cold water.
The discovery which Carnot made was that THE DIFFERENCE IN THE TEMPERATURES BETWEEN THE HOT AND THE COLD RESERVOIRS DETERMINE HOW WELL A HEAT ENGINE WOULD WORK.
Sadi Carnot was a French engineer, He proposed a theoretical thermodynamic cycle in 1824. In his cycle, Said hold that the efficiency of a heat engine depends on the temperature difference between its hot reservoir and cold reservoir.