Question

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?

Answer 1

The mass of the iceberg is approximately 1.468 x 10^18 kg. The amount of heat transfer needed to melt the iceberg is approximately 4.90 x 10^23 J. It would take approximately 17,702 years for sunlight alone to melt ice this thick.

Step-by-step explanation:

In order to calculate the mass of the iceberg, we need to use the formula:

Mass = Volume x Density

First, let's convert the dimensions of the iceberg to meters:

Length = 160 km = 160,000 m

Width = 40.0 km = 40,000 m

Height = 250 m

Now we can calculate the volume of the iceberg:

Volume = Length x Width x Height = (160,000 m)(40,000 m)(250 m) = 1.6 x 1015 m3

Next, we can calculate the mass:

Mass = Volume x Density = (1.6 x 1015 m3)(917 kg/m3) = 1.468 x 1018 kg

Therefore, the mass of the iceberg is approximately 1.468 x 1018 kg.

To calculate the amount of heat transfer needed to melt the iceberg, we can use the formula:

Heat Transfer = Mass x Latent Heat of Fusion

Latent Heat of Fusion for ice is 334,000 J/kg

Heat Transfer = (1.468 x 1018 kg)(334,000 J/kg) = 4.90 x 1023 J

Therefore, the amount of heat transfer needed to melt the iceberg is approximately 4.90 x 1023 J.

To calculate the number of years it would take sunlight alone to melt ice this thick, we need to consider the amount of energy absorbed by the ice from the sunlight. The energy absorbed can be calculated using the formula:

Energy Absorbed = Area x Power x Time

Area = Length x Width = (160,000 m)(40,000 m) = 6.4 x 1012 m2

Power = 100 W/m2

Time = 12.00 hours = 12.00 x 3600 seconds = 43,200 seconds

Now we can calculate the energy absorbed:

Energy Absorbed = (6.4 x 1012 m2)(100 W/m2)(43,200 s) = 2.7648 x 1019 J

Finally, we can calculate the number of years:

Number of Years = Heat Transfer / Energy Absorbed = (4.90 x 1023 J) / (2.7648 x 1019 J) = 1.7702 x 104 years

Therefore, it would take approximately 17,702 years for sunlight alone to melt ice this thick.

Answer 2

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

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

(c) 44.5 year.

Step-by-step 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.