Question

In 2000, a gargantuan iceberg broke away from the Ross Ice Sheet in Antarctica. It was approximately a rectangle with dimensions 295km long, 37.0km wide, and 250.0m thick.

What is the mass of this iceberg, given that the density of ice is 917kg/m3 ?

m=

How much heat transfer in joules is needed to melt the iceberg?

Q=

How many years would it take sunlight alone to melt ice this thick if the ice absorbs an average of 117W/m

2,12.0h per day?

t=

Answer 1

Length of the iceberg, L = 295 km = 295 x 1000 m

Width of the iceberg, W = 37 km = 37 x 1000 m

Thickness of the iceberg, H = 250 m

(a) Volume of the iceberg, V = L x W x H

=  295 x 1000 x 37 x 1000 x 250 = 2.73 x 10^12 m^3

density of ice, = 917 kg/m^3

Hence, mass of the iceberg, M = V*

= 2.73 x 10^12 x 917 = 2.50 x 10^15 kg (Answer)

(b) Latent heat of ice, L = 334000 J/kg

Therefore, quantity of heat required to melt this iceberg, Q = M*L

= 2.50 x 10^15 x 334000

= 8.35 x 10^20 Joule (Answer)

(c) Surface area of the iceberg, A = L x W = 295 x 1000 x 37 x 1000 = 1.09 x 10^10 m^2

So, quantity of heat absorbed by the iceberg per day, q = 117 x 12 x 60 x 60 x 1.09 x 10^10 Joule.

So, no. of days required to melt the iceberg, n = Q / q

= (8.35 x 10^20) / (117 x 12 x 60 x 60 x 1.09 x 10^10)

= 15156 days

= 41.5 years (Answer)