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Chemomechanics
Chemomechanics
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However, at the same time, the heat from the cup would also reach the ice, which would make it melt faster, cooling the water faster.

The reasoning goes awry here. The heat from the cup can reach the floating ice only through the water. In other words, the hotter cup makes the adjacent water hotter. It can't simultaneously be argued to be colder.

I do agree that the hotter cup melts the ice faster, though. Specifically, the water adjacent to the ice is at approximately 0°C. Because the water next to the hotter cup is hotter, the hotter cup increases the temperature gradient (i.e., the spatial temperature difference between the ice and the cup) and drives a larger heat flux that makes the ice melt faster. Nevertheless, the water temperature is always hotter with the hotter cup. Heat transfer can only respond to temperature gradients; it cannot "gain on" a larger gradient as if it had intertiainertia.

However, at the same time, the heat from the cup would also reach the ice, which would make it melt faster, cooling the water faster.

The reasoning goes awry here. The heat from the cup can reach the floating ice only through the water. In other words, the hotter cup makes the adjacent water hotter. It can't simultaneously be argued to be colder.

I do agree that the hotter cup melts the ice faster, though. Specifically, the water adjacent to the ice is at approximately 0°C. Because the water next to the hotter cup is hotter, the hotter cup increases the temperature gradient (i.e., the spatial temperature difference between the ice and the cup) and drives a larger heat flux that makes the ice melt faster. Nevertheless, the water temperature is always hotter with the hotter cup. Heat transfer can only respond to temperature gradients; it cannot "gain on" a larger gradient as if it had intertia.

However, at the same time, the heat from the cup would also reach the ice, which would make it melt faster, cooling the water faster.

The reasoning goes awry here. The heat from the cup can reach the floating ice only through the water. In other words, the hotter cup makes the adjacent water hotter. It can't simultaneously be argued to be colder.

I do agree that the hotter cup melts the ice faster, though. Specifically, the water adjacent to the ice is at approximately 0°C. Because the water next to the hotter cup is hotter, the hotter cup increases the temperature gradient (i.e., the spatial temperature difference between the ice and the cup) and drives a larger heat flux that makes the ice melt faster. Nevertheless, the water temperature is always hotter with the hotter cup. Heat transfer can only respond to temperature gradients; it cannot "gain on" a larger gradient as if it had inertia.

Source Link
Chemomechanics
Chemomechanics
  • 28.1k
  • 7
  • 46
  • 114

However, at the same time, the heat from the cup would also reach the ice, which would make it melt faster, cooling the water faster.

The reasoning goes awry here. The heat from the cup can reach the floating ice only through the water. In other words, the hotter cup makes the adjacent water hotter. It can't simultaneously be argued to be colder.

I do agree that the hotter cup melts the ice faster, though. Specifically, the water adjacent to the ice is at approximately 0°C. Because the water next to the hotter cup is hotter, the hotter cup increases the temperature gradient (i.e., the spatial temperature difference between the ice and the cup) and drives a larger heat flux that makes the ice melt faster. Nevertheless, the water temperature is always hotter with the hotter cup. Heat transfer can only respond to temperature gradients; it cannot "gain on" a larger gradient as if it had intertia.