01-14-2011, 04:00 PM

Richard111,

Hi. You have done some calculations to come up with an estimated 334 quadrillion joules, or 334 billion MJ, of heat necessary for the isothermal melting of 1 cubic km of glacial ice that begins at a uniform temperature of 0.0°C.

One of your premises is that 334,000 joules are necessary for 1 kg of ice at the said temperature. And you have stated that ice is 1/1.1 times or .9090909 times as dense as water, so that the amount of ice to be melted per cubic km of water that is required is 1.1 cubic km.

1g of liquid water takes up 1 cubic cm. Thus, with your density conversion factor, 1 cubic cm of glacial ice has mass of .9090909 g.

The number of cubic cm in a cubic km is 100,000 * 100,000 * 100,000 = 1 million billion, or 1 quadrillion, cubic cm. 1 quadrillion cm^3 * .9091g/cm^3 = 909.0909 trillion grams or 909.0909 billion kg.

A cubic km of glacial ice, according your density assumption, contains 909.0909 billion kg.

(909.0909 billion kg / cubic km of ice) * (.334 MJ/kg) = 303.6364 billion MJ / cubic km of ice.

So you're off by a little bit on the megajoules-per-cubic-km-of-ice calculation.

You then have to figure out the volume of the ice-equivalent of the amount of water you need. The needed water, per your assumptions, is 361,132.4 cubic km. This corresponds to a volume of 361,132.4 * 1.1 = 397,245.64 cubic km of glacial ice.

397,245.64 cubic km * 303.6364 billion MJ / cubic km = 120.6182 quadrillion MJ in total. That is what you reported.

So even though you had the wrong intermediate figure, you ended up with the right final answer for MJ. Apparently, the way you calculated is not exactly as you reported.

But it's still interesting findings!

RTF

Hi. You have done some calculations to come up with an estimated 334 quadrillion joules, or 334 billion MJ, of heat necessary for the isothermal melting of 1 cubic km of glacial ice that begins at a uniform temperature of 0.0°C.

One of your premises is that 334,000 joules are necessary for 1 kg of ice at the said temperature. And you have stated that ice is 1/1.1 times or .9090909 times as dense as water, so that the amount of ice to be melted per cubic km of water that is required is 1.1 cubic km.

1g of liquid water takes up 1 cubic cm. Thus, with your density conversion factor, 1 cubic cm of glacial ice has mass of .9090909 g.

The number of cubic cm in a cubic km is 100,000 * 100,000 * 100,000 = 1 million billion, or 1 quadrillion, cubic cm. 1 quadrillion cm^3 * .9091g/cm^3 = 909.0909 trillion grams or 909.0909 billion kg.

A cubic km of glacial ice, according your density assumption, contains 909.0909 billion kg.

(909.0909 billion kg / cubic km of ice) * (.334 MJ/kg) = 303.6364 billion MJ / cubic km of ice.

So you're off by a little bit on the megajoules-per-cubic-km-of-ice calculation.

You then have to figure out the volume of the ice-equivalent of the amount of water you need. The needed water, per your assumptions, is 361,132.4 cubic km. This corresponds to a volume of 361,132.4 * 1.1 = 397,245.64 cubic km of glacial ice.

397,245.64 cubic km * 303.6364 billion MJ / cubic km = 120.6182 quadrillion MJ in total. That is what you reported.

So even though you had the wrong intermediate figure, you ended up with the right final answer for MJ. Apparently, the way you calculated is not exactly as you reported.

But it's still interesting findings!

RTF