The enthalpy of fusion of water is 6.01 kJ/mol Sunlight striking Earth\'s surfac

Question

The enthalpy of fusion of water is 6.01 kJ/mol Sunlight striking Earth's surface supplies 168 W per square meter (1 W = 1 watt = 1 J/s). Assuming that melting of ice is only due to energy input from the Sun, calculate how many grams of ice could be melted from a 1.00 square meter patch of ice over a 12-hour day. The specific heat capacity of ice is 2.032 J/g degree C. If the initial temperature of a 1.00 square meter patch of ice is -1 degree C, what is its final temperature after being in sunlight for 12 hours, assuming no phase changes and assuming that sunlight penetrates uniformly to a depth of 1.00 cm?

Explanation / Answer

volume of ice patch = a*l

                    = 1*(10^2)^2*1 = 10^4 ml

let us take density of ice = 1 g/cc

mass of ice = d*v =10^4*1 = 10^4 g

q = m*s*DT

q = heat absorbed from sunlight = 168*12*60*60 = 7.26*10^6 joule

7.26*10^6 = 10^4*2.032*(x--1)

x = final temperature = 356.3 c

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