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Why should the ice melt faster in gas, but actually it melts faster in liquid?
Answer 1:

Well, let's boil this question down (see what I did there?): the rate at which ice melts depends on how quickly it's losing heat. Now, this heat loss depends on two factors: the temperature of its environment and how quickly its environment is able to conduct heat away from the ice.

So, let's say you have two pieces of ice, one just sitting out in air (at room temperature) and one sitting in a glass of water (also at room temperature). Now, the temperature of both environments (the air and the water) is the same, so the only think will determine which block of ice melts faster is which environment is able to conduct heat away from the ice. As you noted, the ice floating in water will end up melting faster, and that's because water is a much better conductor of heat than air is.

But what if the temperatures of the environments are different? Say you put one piece of ice in an oven and another in room temperature water. Then even though the water conducts heat better, because the air in the oven is so much hotter, the ice in the oven will still melt much faster. So ice can melt faster in gas than in liquid, but it just depends on the temperatures of the liquid and gas! Sebastian Fischetti

Answer 2:

This is a great question! Something that we need to consider is a property called the thermal conductivity. This is a measure of how well a material conducts energy through heat. The units of thermal conductivity are watt per (meter Kelvin), which is a useful way of saying how much power (energy per time) can be conducted per distance at a particular temperature. Looking up values, we find that the thermal conductivity for air is about 0.025 W/m•K, while that for liquid water is 0.56 W/m•K. The value for liquid is over an order of magnitude higher! Thus, we expect ice to melt faster (transfer its energy better) in liquid water than in air.

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