Question

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

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

Step-by-step solution

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: \(0.1 \times 2.1 \times 10^{8} \, \mathrm{kg} = 2.1 \times 10^{7} \, \mathrm{kg}.\)

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: \(\text{Heating required} = 2.1 \times 10^{7} \, \mathrm{kg} \times 334 \, \mathrm{kJ / kg}.\)

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 = \( (\,2.1 \times 10^7 \, kg \times 334 \, kJ/kg \,) / 10^9 \, kJ/TJ\).

Key concepts

Latent Heat

Latent heat is an essential concept in thermodynamics. It refers to the amount of heat required to change the state of a substance without changing its temperature. For instance, transforming ice into water involves latent heat, more specifically, latent heat of fusion. This process requires a significant amount of energy to break the bonds between the ice molecules.
A real-world example of latent heat is observed in the melting of icebergs. In our exercise, we're melting a portion of an iceberg. The latent heat of fusion for ice is valued at 334 kJ/kg, meaning this is the energy needed to melt 1 kg of ice without a temperature change.

• Total iceberg mass: 210,000 metric tons
• Part melted: 10%
• Latent heat of fusion of ice: 334 kJ/kg

In calculations, the latent heat is multiplied by the mass of the ice involved to ascertain the energy needed for melting. Understanding latent heat allows us to appreciate the large energy requirements in phase changes.

Iceberg Melting

Melting an iceberg involves a fascinating interplay of natural forces and thermodynamic principles. Icebergs, massive chunks of floating ice, naturally melt when exposed to warmer ocean currents or air temperatures. In our exercise, we take a more targeted approach by possibly using mechanical or artificial means. Melting deals with changing the ice state to liquid, demanding substantial heat due to water's high latent heat. The iceberg in question weighs a colossal 210,000 metric tons, and we aim to melt 10% of it, equating to a whopping 21,000 metric tons of ice. However, naturally melting an iceberg or attempting to sink one through direct heating can be exceptionally challenging due to:

• The massive size and thermal inertia of icebergs
• The vast amount of heat required
• The cooler temperatures of surrounding water

Understanding iceberg melting helps in grasping the impracticality of certain iceberg management techniques.

Heat Transfer

Heat transfer is a fundamental concept crucial in explaining how energy drives changes like ice melting. It involves the movement of thermal energy from a hotter region to a cooler one and can occur through conduction, convection, or radiation. In terms of iceberg melting, heat is transferred from warm sources to the cold ice. Conduction occurs when heat sources are placed directly on or in the ice, allowing energy transfer through contact. Convection may happen via warm water currents transferring heat, and radiation contributes through sunlight warming the ice's surface. The exercise shows heat being used to melt an iceberg, which necessitates:

• Understanding and calculating energy flow
• Taking into account efficient heat delivery methods
• Recognizing environmental conditions affecting transfer

An essential part of solving thermodynamics problems is recognizing heat transfer as the vehicle for energy changes and using it to calculate precise needs, like the terajoules needed to melt the iceberg portion in question.