Silicates of \(\text{Cu}\) and \(\text{Fe}\)
Copper matte is primarily composed of copper and iron sulphides. It is obtained during the process of smelting copper ores. The smelting process involves heating copper ores in the presence of a flux to separate impurities. The resultant mixture, known as matte, typically contains copper and iron in the form of their sulphides (\(\text{Cu}_2\text{S}\) and \(\text{FeS}\)).
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity)