Can someone explain why, when sugar is burnt aerobically, it yields more energy than if it is burnt in anaerobic conditions?

My thesis is that in aerobic conditions, there is an abundant supply of oxygen which can burn the sugar and thus, creating ATP (energy) which is limited by the amount of sugar present. However, in anaerobic conditions, there isn't that supply of oxygen to readily burn the sugar, thus, ATP is not produced in that abundance as was the first case scenario.
Is that concept right?

yes, in the case of limited oxygen, one gets other products (other than CO2 and water). THose products waste the energy stored in sugar to making those products.

Yes, your understanding is generally correct. When sugar is burnt aerobically, it undergoes a process called cellular respiration, where it reacts with oxygen to produce ATP (adenosine triphosphate), which is the primary energy currency of cells. This process occurs in the presence of abundant oxygen, which allows for the complete oxidation of sugar molecules, resulting in a greater yield of energy in the form of ATP.

In contrast, under anaerobic conditions, sugar is broken down through a process called fermentation. During fermentation, sugar molecules are partially oxidized without the presence of oxygen, leading to the production of a small amount of ATP. However, since the oxidation is incomplete, the overall energy yield is lower compared to aerobic respiration.

In aerobic conditions, the presence of oxygen enables the sugar molecules to go through multiple stages of cellular respiration, including glycolysis, the Krebs cycle, and the electron transport chain. These stages produce a larger number of ATP molecules per sugar molecule compared to anaerobic fermentation.

To summarize, the key difference between aerobic and anaerobic processes lies in the availability of oxygen. Aerobic respiration can efficiently extract energy from sugar molecules due to the complete oxidation made possible by the presence of oxygen. In contrast, anaerobic fermentation occurs in the absence of oxygen, resulting in incomplete oxidation and lower energy production.