(A) The extraction of aluminum is achieved through the Hall-Héroult process, where Al2O3 is obtained as a precipitate by bubbling CO2 through a solution of sodium aluminate, resulting in the reaction:
\(2\text{Na}[ \text{Al}(\text{OH})_4](\text{aq.}) + \text{CO}_2 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + 2\text{Al}(\text{OH})_3(\downarrow) \text{ or } \text{Al}_2\text{O}_3 \cdot 2\text{H}_2\text{O} (\text{ppt})\)
(B) The electrolytic reduction of pure alumina occurs in a steel box lined with carbon (cathode), along with the presence of cryolite (Na3AlF6) and fluorspar (CaF2), which decrease the melting point and enhance the electrolyte's conductivity.
(C) In the electrolysis process of the Hall-Héroult method, graphite rods serve as anodes. At the cathode, aluminum ions are reduced:
\(\text{Al}^{3+} + 3e^- \rightarrow \text{Al}\)
At the anode, the liberated oxygen reacts with the carbon of the anode to form CO and CO2:
\(\text{C} + \text{O}_2^- \rightarrow \text{CO} + 2e^-\)
\(\text{C} + 2\text{O}_2^- \rightarrow \text{CO}_2 + 4e^-\)
(D) In this context, the cathode consists of a steel vessel with a carbon lining.
A parallel plate capacitor with plate area \(A\) and plate separation \(d = 2\) m has a capacitance of \(4\mu F\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K = 3\) (as shown in the figure) will be:
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of \( 60^\circ \) by a force of 10 N parallel to the inclined surface. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is:
[Given: \( g = 10 \) m/s\( ^2 \), \( \mu_s = 0.1 \)]