? q = Total mass of ice on the planet, for ease we’ll round it up slightly to 30 septillion grammes.
? ΔTemp. The current year round average global temperature across Antarctica is approx 248K but the ice didn’t form at this temperature, most of it formed during the last million years when the average global temperature was 242°C. The same principle for Greenland gives and average ice temperature of 260K°C. Given that the mass of Antarctic ice is none times that of Greenland then the global average ice temp will be 244K. Glaciers and the Arctic ice-sheet are minute in comparison and will have so little bearing on ΔTemp that I’ve ignored them.
? Cp = energy needed to raise 1g of ice by 1K.
Energy required to raise the temp of ice to melting point (but not to melt it) is…
30^24 x 42 x 2.06 = 2.596^27J
Next we have to add the energy required to melt the ice…
? q = 30^24g
? Molar mass of water = 18gmol-1
? Molar heat of fusion (hfus) = 6.02kj/mol
Energy required is…
(30^24/18) x 6.02 = 10.033^27J
Add the two together gives us the total energy required to melt all the ice: 12.6^27J.
This figure is approx 8,750 times the total heat energy of the atmosphere (5.01^21J/K at 288K = 1.442^24J) and approx 8 times the energy in the oceans (5.6^24J/K at 291K = 1.630^27J).
If Earth were to effectively be encapsulated with no incoming or outgoing energy then there wouldn’t be enough heat energy in all the oceans and the atmosphere to melt the ice on the planet. Earth isn’t encapsulated and receives 174PW of energy from the Sun each year, over a very long period of time this would be enough to melt all the ice.
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RE: YOUR ADDED DETAILS
Given that the heat content of the oceans and atmosphere isn’t enough to melt all the ice then we’d reach a hypothetical position where the oceans froze solid and the atmosphere was at absolute zero, and the heat extracted from them wouldn’t have melted the ice.
Over many thousand of years (about 6,000) the oceans would reach a state of equilibrium if Earth were to be a closed system. If all of the energy in all of the oceans were directed to melting the ice then it still wouldn’t be enough to melt it, largely because of the high molar heat of fusion. What we’d end up with is an equilibrated atmosphere, ocean and cryosphere at around 273K or slightly less. This would means the atmosphere would cool by approx 15K, the oceans approx 17K and the cryosphere warm by approx 29K.
The only way to melt all of the ice would be to introduce more energy, which is what the Sun does. The alternative, if we stick with a closed system, would be to extract energy from the ground as well as the oceans and atmosphere. Perhaps something like the first 500m to 1000m would provide the additional energy required to finally melt all the ice.
A is not entirely correct. He forgot to mention that it takes 80 calories to turn 1 gram of ice at 0degC into 1 gram of water of the same temperature. This means that melting the ice consumes much more energy than warming ice or water though the temperature does not change until all ice has melted.
So in your experiment all you have to know is how much ice there is on earth (in grams) and then multiply it by 80 and you have a rough estimate of how many calories that would take. But you still have to consider all the permafrost soil plus the amount of energy needed to to warm all the ice from the current temperature to 0degC
As it takes X amount of heat to raise the temperature of a unit of ice to its melting point, that's where to start. Then you have to quantify exactly how much ice there is on the planet. Then there's a 'time' element to introduce to the equation. Any good math major could answer this question. I was a history major so I'm, no help.
At first, the Earth which had the ice stollen by aliens would be warmer, because of the cooling effect of the latent heat of fusion of water, but both planets would settle on the same equilibrium.
First you need to know how many grammes of ice there are, next you need to know the average number of degrees Celsius it all is below zero. Multiply the two numbers together and you'll have your answer in calories. This is because it takes one calorie to raise a gramme of water by 1C
I am much too lazy to even attempt to do the math, but lets just say the amount of latent heat required to change all that ice to water is absolutely huge, it would take thousands of years to turn that ice into water before you even raised 1 degree C.
I don't do 'IF' questions especially involving aliens.
WHY < WHY WOULD YOU DO THAT NO ICE FOR MY MARGARETA .
Basically... imagine all the "permanent" natural ice in the world melted. All the glaciers, all of Antarctica, all of the Arctic sea ice. Approximately how much of a temperature change, in terms of atmospheric temperature, would all that ice melting "use up"?
Or, to put it another way... imagine 2 Earths with identical atmospheres, solar inputs, et cetera. One has all of its global warming concentrated on ice melting, and the other has all of the "permanent" ice stolen by aliens and replaced with an equal mass of ice-cold water. How much warmer would the latter Earth be at the end of the process?
