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

The properties of liquid sodium that make it suitable as a coolant in a nuclear reactor include high thermal conductivity, high boiling point and low melting point, chemical stability, and a low neutron absorption cross-section. As for its viscosity, cohesive forces and momentum transfer are the main contributors. Viscosity decreases with increasing temperature due to an increase in thermal energy, which enables atoms and ions to overcome the attractive forces more easily, and a decrease in cohesive forces, leading to less resistance to flow.

Step-by-step solution

To determine the properties of liquid sodium that make it suitable as a coolant in a nuclear reactor, we should consider the following aspects: - High thermal conductivity: High thermal conductivity allows the coolant to efficiently transfer heat from the reactor core to the heat exchangers. - High boiling point and low melting point: A high boiling point ensures that the coolant remains in the liquid phase at the high temperatures in the reactor core. A low melting point allows the coolant to be easily handled during maintenance or refueling. - Chemical stability: The coolant should be chemically stable and not react with the reactor materials or decay products. - Low neutron absorption cross-section: To minimize the impact on the reactor's neutron balance, the coolant should have a low neutron absorption cross-section. #a_Title# (b) Viscosity of Liquid Sodium and Temperature

The table provided gives us the relationship between the viscosity of liquid sodium and its temperature. We see that as the temperature increases, the viscosity decreases. #b_Title# (b.1) Forces Contributing to Viscosity

Viscosity arises from the internal resistance to flow caused by forces within the liquid. In the case of liquid sodium, these forces can be attributed to: - Cohesive forces: These are the attractive forces between the sodium atoms, such as van der Waals forces and metallic bonding. These forces contribute to the resistance to flow in the liquid metal. - Momentum transfer: Liquid sodium is composed of ions (Na+) and free electrons. The viscosity of liquid metals can also be attributed to the momentum transfer between ions and electrons as they interact with each other. #b_Title# (b.2) Why viscosity decreases with increasing temperature

Viscosity decreases with increasing temperature due to the following reasons: - Increase in thermal energy: As temperature increases, the thermal energy of the atoms and ions in the liquid sodium increases, allowing them to overcome the attractive forces between them more easily. This results in a decrease in resistance to flow. - Decrease in cohesive forces: Temperature rise leads to weakening of the cohesive forces between sodium atoms. Weaker forces mean less resistance to flow which, eventually, leads to a decrease in viscosity. Hence, the given data shows a decrease in viscosity with increasing temperature for liquid sodium.