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Chapter 23: Problem 12

Icebergs in the North Atlantic present hazards to shipping (see Fig. 23-30), causing the length of shipping routes to increase by about \(30 \%\) during the iceberg season. Strategies for destroying icebergs include planting explosives, bombing, torpedoing, shelling, ramming, and painting with lampblack. Suppose that direct melting of the iceberg, by placing heat sources in the ice, is tried. How much heat is required to melt \(10 \%\) of a 210,000 -metric-ton iceberg? (One metric ton \(=\) \(1000 \mathrm{~kg} .)\)

Short Answer

Expert verified
The heat required to melt 10% of a 210,000 metric-ton iceberg is approximately 7 TJ.

Step by step solution

01

Calculate the mass to be melted

First calculate the mass of the iceberg that needs to be melted. As given, this is 10% of a 210,000-metric-ton iceberg. The iceberg mass is: \(210,000 \,\, \text{Mt} = 210,000 \times 1,000 \, \mathrm{kg} = 2.1 \times 10^{8} \,\, \mathrm{kg}.\) So, the mass to be melted is: \(0.1 \times 2.1 \times 10^{8} \, \mathrm{kg} = 2.1 \times 10^{7} \, \mathrm{kg}.\)
02

Calculate the required heat

Next, use the latent heat of fusion of ice (334kJ/kg) to calculate the required heat. This can be found using the formula: \(\text{Heating required} = \, \text{mass to be melted} \times \, \text{Latent heat of fusion of ice}\) So: \(\text{Heating required} = 2.1 \times 10^{7} \, \mathrm{kg} \times 334 \, \mathrm{kJ / kg}.\)
03

Convert the units

To make final answer more readable, convert kJ to TJ (TeraJoules). As 1 TJ \(=\) \(10^{9} \, kJ\), perform the conversion: Heating required = \( (\,2.1 \times 10^7 \, kg \times 334 \, kJ/kg \,) / 10^9 \, kJ/TJ\).

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Most popular questions from this chapter

What mass of steam at \(100^{\circ} \mathrm{C}\) must be mixed with \(150 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\), in a thermally insulated container, to produce liquid water at \(50^{\circ} \mathrm{C}\) ?

The average rate at which heat flows out through the surface of the Earth in North America is \(54 \mathrm{~mW} / \mathrm{m}^{2}\) and the average thermal conductivity of the near surface rocks is \(2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Assuming a surface temperature of \(10^{\circ} \mathrm{C}\), what should be the temperature at a depth of \(33 \mathrm{~km}\) (near the base of the crust)? Ignore the heat generated by radioactive elements; the curvature of the Earth can also be ignored.

Calculate the work done by an external agent in compressing \(1.12 \mathrm{~mol}\) of oxygen from a volume of \(22.4 \mathrm{~L}\) and \(1.32\) atm pressure to \(15.3 \mathrm{~L}\) at the same temperature.

Consider that \(214 \mathrm{~J}\) of work are done on a system, and \(293 \mathrm{~J}\) of heat are extracted from the system. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of \((a) W,(b) Q\), and \((c) \Delta E_{\text {int }} ?\)

\((a)\) A monatomic ideal gas initially at \(19.0^{\circ} \mathrm{C}\) is suddenly compressed to one-tenth its original volume. What is its temperature after compression? (b) Make the same calculation for a diatomic gas.
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