Which will lower the temperature of warm water more than a piece of ice or the same amount of zero temperature water?

We will consider the solution to this problem from the point of view of heat energy consumption.

When adding cold water to warm water, part of the energy of warm water will be spent on heating cold water until all the water is at the same temperature.

When adding a piece of ice to warm water, some of the energy of the warm water will be spent on:

1) melting ice;

2) heating cold water until all the water is at the same temperature.

Since cold water and a piece of ice, according to the condition of the problem, have the same mass, it is obvious that in the second case (a piece of ice) more energy will be expended, which means that the resulting mixture will have a lower temperature.

Answer: a piece of ice will lower the temperature of the thermal water more than that amount of zero temperature water.