Question

Icebergs in the North Atlantic present hazards to shipping, causing the lengths of shipping routes to be increased by about$\text{30\%}$during the iceberg season. Attempts to destroy icebergs include planting explosives, bombing, torpedoing, shelling, ramming, and coating with black soot. Suppose that direct melting of the iceberg, by placing heat sources in the ice, is tried. How much energy as heat is required to melt $\text{10\%}$of an iceberg that has a mass of $200000\text{metric\hspace{0.17em}tons}$? (Use $\text{1metricton}=\text{1000kg}$)

Short answer

The amount of energy that is required as heat to melt of an iceberg is $6.7\times {10}^{12}\text{J}$.

Step-by-step solution

Identification of given data

i) Rate of shipping of iceberg increased to $30\%$.

ii) Percentage of iceberg required to melt is $10\%$.

iii) Mass of an iceberg $m=200\text{000metrictons}$,

iv) Latent heat of fusion of ice $L_f=333\text{kJ/kg}$,

v) The value of metric ton in kilogram, $\text{1metricton}=\text{1000kg}$

Understanding the concept of conduction due to heat transfer

In the given problem, the melting of an iceberg is required due to thermal conduction in the iceberg. This brings latent heat into consideration. When energy is released by a body to change from one given state to the other required state, the specific heat involved in the process is called the latent heat of fusion of the body. This latent heat is released by the body to impose thermal conduction as heat to the iceberg that will start the phase change process in it. The required heat needed to transfer to the iceberg to initiate the process is the amount of conducted heat released by it.

Formulae:

The heat energy released by the body, $Q=L_{f}m$ …(i)

Where $L_f$, is the latent heat of fusion, $m$ is the mass of the substance.

Determining the energy released to melt the given mass of iceberg by 10%

It is required to melt only$10\%$of the total given mass of the iceberg. Thus, the amount of heat released by the body as heat to melt the iceberg can be given using the given data in equation (i) as follows:

$\begin{array}{c}Q=L_f\left(10\%m\right)\\ =\left(333\text{kJ/kg}\right)\left(\frac{10}{100}\right)\left(200000\text{metrictons}\right)\left(1000\text{kg}\right)\\ =6.7\times {10}^{12}\text{J}\end{array}$

Hence, the value of the required energy is $6.7\times {10}^{12}\text{J}$.