In 1986, an enormous iceberg broke away from the Ross Ice Shelf in Antarctica. It was an approximately rectangular prism 160 km long, 40.0 km wide, and 250 m thick.

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

(b) How much heat transfer (in joules) is needed to melt it?

(c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100W/m2, 12.00 h per day?

(a) 1.6 * 10¹² * 917 = 1.47 * 10¹⁵ kg.

(b) 336 * 1.47 * 10¹⁵ = 4.94 * 10¹⁷ kJ.

(c) 44.5 year.

Explanation:

Density (D) = mass (M) / Volume (V)

D = M/V ... Equation 1

Where D = 917 kg/m³, V = volume of the iceberg = volume of rectangular prism = Length (L) * width (W) * Height (H).

(a)

Where L = 160 km = 160 * 1000 = 160000 m

W = 40 km = 40 * 1000 = 40000 m

H = 250 m.

∴ Volume = 160000 * 40000 * 250 = 1.6 * 10¹² m

Therefore, M = D * V

M = 1.6 * 10¹² * 917 = 1.47 * 10¹⁵ kg.

(b)

Q = m * l

Where Q = heat needed to melt the ice, m = mass of ice, l = specific latent heat of fusion of ice.

The specific latent heat of fusion of ice = 366 kJ/kg, m = 1.47 * 10¹⁵ kg

Q = 336 * 1.47 * 10¹⁵ = 4.94 * 10¹⁷ kJ.

(c)

Q/t = A*Pₐ ... equation 2 making t the subject of formula in equation 2

t = Q / (A*Pₐ) ... Equation 3

Where

Pₐ = 100 W/m², A = area of the ice = 160000 * 40000 = 6.4 * 10 ⁹ m², Q = 4.94 * 10¹⁷ kJ. = 4.94 * 10²⁰ J.

Substituting these values in equation 3.

t = (4.49 * 10²⁰) / (6.4 * 10⁹ * 100)

t = 7.02 * 10⁸ seconds = (7.02 * 10⁸) / 3600 = 195000 hours.

If it absorbs energy from the sun for 12 hours per day,

195000 hours = (195000/12) day

= 16250 days.

If 365 days = 1 year,

16250 days = (16250/364) days

= 44.5 year.

It will take the sun alone 44.5 years to melt the ice.