Question

In a certain type of nuclear reactor, liquid sodium metal is employed as a circulating coolant in a closed system, protected from contact with air or water. Much like the coolant that circulates in an automobile engine, the liquid sodium carries heat from the hot reactor core to heat exchangers. (a) What properties of the liquid sodium are of special importance in this application? (b) The viscosity of liquid sodium varies with temperature as follows: $$ \begin{array}{ll} \hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & \text { Viscosity }\left(\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\right) \\ \hline 100 & 7.05 \times 10^{-4} \\ 200 & 4.50 \times 10^{-4} \\ 300 & 3.45 \times 10^{-4} \\ 600 & 2.10 \times 10^{-4} \\ \hline \end{array} $$ What forces within the liquid sodium are likely to be the major contributors to the viscosity? Why does viscosity decrease with increasing temperature?

Short answer

In summary, liquid sodium is suitable as a circulating coolant in a nuclear reactor due to its high thermal conductivity, low neutron absorption cross-section, high boiling point, and non-corrosive nature. The major contributors to liquid sodium's viscosity are cohesive forces resulting from strong interactions between positive metal ions and delocalized electrons. The viscosity decreases with increasing temperature as the kinetic energy of the particles increases, allowing them to overcome attractive forces more easily, thus promoting smoother flow.

Step-by-step solution

Part (a): Properties of liquid sodium

There are several properties of liquid sodium that make it an appropriate choice as a circulating coolant in a nuclear reactor. Some of the properties worth mentioning are: 1. High thermal conductivity: Liquid sodium has excellent heat transfer capabilities, which means it can quickly absorb heat from the reactor core and transfer it to the heat exchangers. 2. Low neutron absorption cross-section: Sodium doesn't easily absorb neutrons, which means it doesn't interfere with the nuclear reactions taking place within the reactor. 3. High boiling point: Liquid sodium has a high boiling point, ensuring that it doesn't evaporate under reactor conditions. 4. Non-corrosive: Sodium doesn't corrode reactor materials, which contributes to the safety and longevity of the reactor.

Part (b): Viscosity of liquid sodium

To identify the forces within the liquid sodium that are likely major contributors to viscosity, we need to understand that viscosity is the internal resistance of fluid to flow. The different forces involved in the viscosity of fluids include: 1. Frictional forces: These occur between the particles within the fluid as they move against one another. 2. Cohesive forces: These forces hold the particles within the liquid together. In the case of liquid sodium, both frictional and cohesive forces contribute to the viscosity. However, since sodium is a metallic element, the cohesive forces, which result from strong interactions between positive metal ions and the delocalized electrons, are likely to be the major contributors to its viscosity. Now, we need to explain why the viscosity of liquid sodium decreases with increasing temperature. As the temperature of the liquid sodium increases, the kinetic energy of the particles also increases. This increased energy allows the particles to overcome the attractive forces between them more easily and move with less resistance. Therefore, the viscosity of the liquid sodium decreases as the temperature increases, meaning it flows more smoothly at higher temperatures.

Key concepts

Liquid Sodium Properties

Liquid sodium is a standout choice for use in a nuclear reactor as a coolant due to a combination of its unique properties. First, its high thermal conductivity is key, as this allows sodium to effectively transfer heat away from the reactor core to heat exchangers efficiently.
This prevents overheating and ensures efficient energy transfer. Furthermore, liquid sodium has a low neutron absorption cross-section. This means it doesn't easily capture neutrons, allowing nuclear reactions to proceed without interference.
Plus, the high boiling point of sodium is crucial because it remains liquid under extreme reactor conditions, reducing the risk of evaporation and providing stability. Finally, sodium is non-corrosive, meaning it does not erode reactor components, promoting safety and a longer lifespan for reactors.

• High thermal conductivity for efficient heat transfer
• Low neutron absorption to support nuclear reactions
• High boiling point for stability
• Non-corrosive to prolong reactor materials

Thermal Conductivity

With respect to thermal conductivity, liquid sodium stands out for its capability to transfer heat efficiently. This property is measured by how well it can conduct thermal energy. In a nuclear reactor, this is vital, as heat generated from nuclear reactions needs to be swiftly transferred to prevent overheating.
Liquid sodium is able to do this far better than other coolant materials. Its thermal conductivity allows for rapid absorption and elimination of heat from the reactor core to the heat exchanger. This ultimately supports the reactor's cooling system in dissipating energy and maintaining operational safety.

• Efficient heat transfer capabilities
• Prevents reactor overheating
• Promotes stable operation by removing heat quickly

Viscosity and Temperature

Viscosity refers to a fluid's resistance to flow. In the case of liquid sodium, viscosity is mainly influenced by frictional and cohesive forces. Frictional forces result from particle movement within the fluid, while cohesive forces involve the attraction between particles due to metal ionic bonds and delocalized electrons.
In metallic liquids like sodium, cohesive forces significantly contribute to viscosity. However, these forces are affected by temperature. As temperature rises, the particles gain kinetic energy, which helps them overcome these forces more easily.
This results in reduced viscosity at higher temperatures, which means that liquid sodium flows smoother and more freely when heated. This behavior is essential for optimizing the coolant flow in reactors as they operate under varying temperature conditions.

• Resistance to flow influenced by internal forces
• Temperature increase reduces cohesive force impact
• Lower viscosity at higher temperatures enhances flow

Nuclear Reactor Safety

In nuclear reactor design, safety is the paramount concern, and the right choice of coolant can significantly impact this. Liquid sodium contributes to reactor safety in several ways. Its low neutron absorption is non-disruptive to nuclear reactions, and its high boiling point ensures stability, preventing unexpected phase changes that could be hazardous.
Additionally, sodium's non-corrosive nature is vital, as it prevents damage to reactor components, reducing the risk of leaks or mechanical failures. Efficient heat transfer characteristics also ensure that the reactor core does not overheat, which is critical in preventing accidents.
By maintaining a balance of operational efficiency and safety, liquid sodium coolant supports both the technical and safety requirements inherent in nuclear power production.

• Prevents interference with nuclear reactions
• Stable under high temperatures
• Reduces risk of mechanical failure due to corrosion
• Efficient heat management crucial for preventing overheating