## 1 Introduction  
Liquid sodium is used in nuclear engineering as a coolant for the first circuit of fast neutron reactors. This metal has high corrosion resistance, low toxicity, and low cost. In addition, it ensures simplicity of technological operations necessary to maintain the specified quality of the coolant during repair work. However, the intense interaction of this metal with water leads to the need of using a second circuit in the reactor system, which prevents the products of their interaction from entering the active zone [1, 2, 3, 4].  
The sodium-potassium liquid eutectic alloy (31.9 atomic %Na [5]) has found its application in the second circuit of a fast neutron nuclear reactor. Also, this coolant is used in low-power space nuclear stations. The very low melting point of the eutectic Na-K alloy (\(-12.3\)\({}^{\circ}\)C) allows for the simplification of the design and makes the operation of the nuclear power system easier [6, 7].  
In addition, the liquid Na-K is employed in many other branches of the industry such as materials' synthesis, biomedicine, microelectronics, catalysis, and sustainable chemistry [8, 9]; this, additionally, makes it interesting to study this alloy at any composition.  
In the current century, the physical properties of Na and Na-K alloy in the liquid state are intensively studied by different theoretical methods [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. A significant part of the aforementioned works was performed in the frameworks of the thermodynamic perturbation theory (TPT) in conjunction with the pseudopotential method. Such an approach was also successfully applied to investigations of other liquid metals and alloys [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34].  
The numerical solving of the Gibbs-Bogoliubov inequality (the variational method) is most widely used among the TPT methods in studies of liquid metals and their alloys(see, for example, Refs. [10; 11; 12; 13; 14; 15; 16; 23; 24; 25; 26; 27; 28; 29]). The main advantage of the variational method is the minimization of the Helmholtz free energy with respect to the parameters of the reference system. This makes it possible to not use any experimental information to determine them.  
Starting from our early work [25], within this method we used an additional minimization with respect to the mean atomic volume that gives an opportunity to avoid input experimental data on density of the melt under consideration. This makes the approach completely free from inputting any experimental data about the system under study, since the only input information required is the values of the pseudopotential parameters, which are determined for pure substances at zero absolute temperature.  
Recently, this approach resulted in very positive results for thermodynamic properties of the equiatomic liquid Na-K, Na-Rb, K-Rb, and Na-Cs binary alloys at \(T=373\) K [15; 16].  
In the present work, we estimate its suitability to investigate the thermophysical properties (namely, the isobaric heat capacity, \(c_{P}\), and isobaric thermal expansion coefficient, \(\alpha_{p}\)) of Na and Na-K coolants in the wide range of temperatures (from 273 K to 1673 K) and compare an accuracy of different pseudopotential models used for calculations.