Transfer of Heat

Question

The surface area of the earth is approx 5.1E14 sq meter of which approx 70% is covered by oceans. Suppose the Antartic ice sheets absorbred 2.2 E24 joules of energy. Consider the ice to be at a uniform temp of 0 C. Determine an approx value for the resulting rise in sea level in meters. It must be one of the aswers listed below, i cannot figure this one out.
.3m or 5m or 18m or 60m.
i really appreciate your time.
joe

Answer 1

This is a dimensional analysis problem.

To solve it you need to convert the energy (2.2 x 10²⁴ J) into the rise of sea levels (in meters).

some useful info from which we can derive the conversion factors

It takes 334 J to melt 1g of ice

The mass of 1 m³ of water is 1000 kg = 1 x 10⁶ g

Now let us set up our calculation. We need to be paying attention to the units

2.2 x 10²⁴ J x ( 1g / 334 J ) x ( 1 m³ / 10⁶ g ) / ( 0.7 x 5.1 x 10¹⁴ m² ) = 18.45 m

Rounding the result to two significant figures we get 18 m