Some of the heat from the water melts the ice when you add it to boiling water. The residual heat cools the hot water while warming the ice-cold water. If you know how much hot water you started with, its temperature, and how much ice you added, you can compute the mixture’s final temperature. The precise manner in which the ice melts and the water cools is controlled by two physical qualities, the specific heat and the heat of fusion.
Particular Heat: The quantity of energy needed to raise the temperature of a substance is measured by its specific heat. For instance, the water warms by 1 degree Celsius when 1 calorie of heat is added to it (1.8 degrees Fahrenheit). The converse is true when the water cools; for every degree Celsius that it loses, each gram of water loses one calorie of heat energy. Different specific temperatures are present in other substances. For instance, it only needs 0.03 calories to raise the temperature of 1 gram of lead.
Thermal Fusion: For each degree Celsius that a container of water cools, one calorie is lost. However, the situation changes as water turns to ice when the temperature drops to zero degrees Celsius (32 degrees Fahrenheit). The amount of heat energy required for this procedure is substantially higher (79.7 calories per gram), and the temperature of the water-ice mixture remains constant until it completely solidifies. The energy that drives a substance through this phase is referred to as the heat of fusion. As water molecules condense into a solid, they expend additional energy. Ice changes temperature once it has formed based on its own specific heat, which is 0.49 calories per degree Celsius.
Energy Change: You need to know the mass of the ice and water as well as the temperature of the water to precisely calculate how the energy changes when you add ice to hot water. For instance, one liter of hot water at 75 degrees Celsius (167 degrees Fahrenheit) has 75,000 more calories of energy than the same quantity of water at 0 degrees Celsius due to its specific heat value (32 degrees Fahrenheit). 100 grams of ice added to water requires 7,970 calories to melt, increasing the total energy to 67,030 calories. The 100 grams absorb 1 calorie per degree of the remaining heat in the hot water as it turns into water, but the heat isn’t “lost”; rather, it has merely shifted into the cold water.
Temperature variation: The water cools from 75 to 67 degrees Celsius while the hot water expends 7,970 calories melting the ice (153 degrees Fahrenheit). While the cold water from the melted ice gains heat, the hot water loses heat. In this illustration, 1,000 grams of water are combined with just 100 grams of ice. As a result, while the cold water warms up by a greater number of degrees, the hot water just slightly loses temperature. When 1,100 grams of water are divided by the 67,030 available calories, the result is a final temperature of roughly 61 degrees Celsius (142 degrees Fahrenheit). Total temperature changes between the hot and cold water are 61 and 14 degrees Celsius, respectively. Remember that the outcome is based on the quantity of ice and hot water you have in the beginning. The hot water won’t be hot enough to melt all the ice if you add a ton of ice to 1,000 grams of water.
