Problem 46 - Chemistry The Science in Context

Question

The reactor-core cooling systems in some nuclear power plants use liquid sodium as the coolant. Sodium has a thermal conductivity of \(1.42 \mathrm{J} /\) \((\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K}),\) which is quite high compared with that of water \(\left.\left[6.1 \times 10^{-3} \mathrm{J} / \mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K}\right)\right] .\) The respective molar heat capacities are \(28.28 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\) and \(75.31 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) .\) What is the advantage of using liquid sodium over water in this application?

Step-by-Step Solution

Answer

Answer: Liquid sodium is preferred over water in reactor-core cooling systems because it has a significantly higher thermal conductivity, which allows it to efficiently transfer heat away from the reactor core and maintain appropriate temperatures. Although water has a higher molar heat capacity, its low thermal conductivity makes it less effective at transferring heat away from the reactor core. Therefore, liquid sodium's superior heat transfer efficiency makes it a better choice for cooling applications in nuclear power plants.

Step 1: Analyze provided properties in the exercise

We are given the following properties for liquid sodium and water: 1. Thermal conductivity of liquid sodium: \(1.42 \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s}\cdot \mathrm{K})\) 2. Thermal conductivity of water: \(6.1 \times 10^{-3} \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K})\) 3. Molar heat capacity of liquid sodium: \(28.28 \mathrm{J}/(\mathrm{mol} \cdot \mathrm{K})\) 4. Molar heat capacity of water: \(75.31 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\)

Step 2: Understand the significance of thermal conductivity in cooling applications

The thermal conductivity of a material defines its ability to conduct heat. High thermal conductivity means that a material can transfer heat quickly, whereas low thermal conductivity means that the heat transfer occurs more slowly. In a cooling system, a high thermal conductivity coolant can efficiently transfer heat away from the reactor core, thus maintaining the appropriate temperature. Comparing the thermal conductivity of liquid sodium and water, we can see that liquid sodium has significantly higher thermal conductivity (\(1.42 \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s}\cdot \mathrm{K})\)) compared to water (\(6.1 \times 10^{-3} \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K})\)). This indicates that liquid sodium transfers heat away from the reactor core more efficiently than water.

Step 3: Understand the significance of molar heat capacity in cooling applications

The molar heat capacity of a material represents the amount of heat required to change the temperature of 1 mole of the substance by 1 K. A material with a high molar heat capacity can absorb more heat without undergoing a significant temperature change, which is necessary for a cooling system to maintain effective cooling. Comparing the molar heat capacity of liquid sodium and water, we can see that water has a higher molar heat capacity (\(75.31\;\mathrm{J}/(\mathrm{mol}\cdot\mathrm{K})\)) compared to liquid sodium (\(28.28\;\mathrm{J}/(\mathrm{mol}\cdot\mathrm{K})\)). This may seem counterintuitive, as it might appear that water would be a better choice since it can absorb more heat for the same temperature change. However, the high molar heat capacity of water combined with its low thermal conductivity means that although water can absorb more heat, it is not as effective at transferring that heat away from the reactor core. As a result, liquid sodium's higher thermal conductivity takes precedence over its lower molar heat capacity in this application.

Step 4: Concluding the advantages of liquid sodium over water

The primary advantage of using liquid sodium over water in reactor-core cooling systems is its significantly higher thermal conductivity. This property allows liquid sodium to transfer heat away from the reactor core more efficiently and maintain the appropriate temperature, despite having a lower molar heat capacity compared to water. Considering the cooling application in nuclear power plants, the overall heat transfer efficiency is more critical than the amount of heat absorbed by the coolant. Therefore, liquid sodium is a better choice for this application due to its superior thermal conductivity.

Key Concepts

Thermal Conductivity

Thermal conductivity is a crucial concept in understanding the efficiency of cooling systems in nuclear reactors. It measures a material's ability to conduct heat, with higher values indicating quicker heat transfer.
The thermal conductivity of various substances can vary significantly. For instance, liquid sodium, often used as a coolant in nuclear reactors, has a thermal conductivity of \(1.42 \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K})\), which is considered high.
In contrast, water, another common coolant, has a much lower thermal conductivity of \(6.1 \times 10^{-3} \mathrm{J}/(\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K})\).

• Higher thermal conductivity means that liquid sodium can transfer heat from the reactor core far more efficiently than water.
• This is essential in maintaining safe operating temperatures and preventing overheating in the reactor.

This contrasts with water, which, due to its low thermal conductivity, would transfer heat away from the reactor core at a much slower rate. Therefore, choosing a coolant with high thermal conductivity, like liquid sodium, is advantageous in nuclear reactor cooling systems.

Molar Heat Capacity

Molar heat capacity describes how much heat energy is needed to raise the temperature of one mole of a substance by one Kelvin. It’s an essential factor in determining how much heat a material can absorb without significantly rising in temperature, which is vital in cooling applications.
Water has a relatively high molar heat capacity of \(75.31\;\mathrm{J}/(\mathrm{mol}\cdot\mathrm{K})\), indicating it can absorb more heat before its temperature increases. In comparison, liquid sodium has a lower molar heat capacity of \(28.28\;\mathrm{J}/(\mathrm{mol}\cdot\mathrm{K})\).

• At first glance, water seems superior because it can absorb more heat for the same amount of temperature change.
• However, when combined with its low thermal conductivity, water is less effective than it appears for transferring heat in reactor cooling systems.

Thus, while a substance with high molar heat capacity can absorb more heat, the key in selecting a coolant is also how effectively it can transfer heat through the system, where thermal conductivity plays a pivotal role.

Coolants in Nuclear Reactors

Coolants in nuclear reactors are materials used to remove heat from the reactor core and control the temperature. Choosing an effective coolant is vital to prevent overheating and ensure the reactor operates safely.

• Liquid sodium is preferred over water as a coolant because of its superior thermal conductivity, allowing efficient heat transfer.
• Even though liquid sodium has a lower molar heat capacity, the efficiency in heat conduction outweighs this disadvantage.
• This makes liquid sodium particularly suitable for fast-breeder reactors, where rapid heat removal is critical.

In essence, in the context of a nuclear reactor, the overall heat transfer efficiency, driven significantly by thermal conductivity, is more advantageous than just the heat absorption capacity, making liquid sodium a top choice.