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Answer :
Final answer:
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.
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.
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Answer:
(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.
