If two bottles containing hot water are placed in a container for cooling purposes and water at 0 degree Celsius is used, instead of melting ice, the cooling is slower. I get that the ice is taking in heat from the surroundings to melt but I'm confused about the water. Why is it slower with water?
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2 Answers
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as long as there is ice left the temperature stays 0°C, so the difference between hot and cold stays large, when you only take water it heats up, tho the difference gets smaller, and the time for cooling depends from the difference of temperature. Also to melt 1g of ice you use more than 300 times as much energy than to warm water 1°.
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All other things being equal, the rate of heat transfer by conduction or convection between objects is proportional to the temperature difference between the objects. The greater the temperature difference, the greater the heat transfer rate.
If the bottle of hot water at say 90 C is placed in a bottle of cold water at 0 C (without ice), heat transfers from the bottle of hot water to the bottle of cold water. As soon as heat starts to transfer, the temperature of the cold water starts to rise and the temperature of the hot water starts to fall. That reduces the temperature difference between the two bottles of water which, in turn, slows the heat transfer rate out of the hot water to the cold water.
Now instead place the bottle of 90 C hot water into a bottle of a mixture of ice and water at 0 C. As heat transfers out of the mixture of ice and water, the temperature initially remains at 0 C as long as ice remains in the mixture. That's because the heat transferring out of the ice component of the mixture, called the latent heat of fusion, first converts ice to water at constant temperature. Since heat transfer out of the ice/water mixture does not initially lower the temperature of the mixture its temperature does not rise while the hot water temperature falls.
We conclude that while the ice is melting, the temperature difference between the hot water and ice water mixture is greater than the temperature difference between the hot and cold water without ice. The greater temperature difference makes the rate of cooling of the hot water faster with the ice water mixture, than with the water without ice.
Hope this helps
