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.
