Which of the following materials will burn the fastest in open air?

A. a log, two feet in diameter
B. two logs, each one foot in diameter
C. a pile of small splinters made from a two-foot diameter log
D. Both logs and the splinters will burn at the same rate.

Given the materials mentioned, the pile of small splinters made from a two-foot diameter log will burn the fastest in open air.

The reason for this is that the smaller the size of the fuel, the larger the surface area to volume ratio, which allows for faster combustion. The small splinters will have the highest surface area to volume ratio, making them more susceptible to rapid burning.

To determine which material will burn the fastest in open air, we need to understand the factors that affect the rate of combustion. The key factors are surface area, volume, and density.

In general, materials with a greater surface area will burn faster because more area is exposed to oxygen, which is necessary for combustion to occur. Additionally, materials with higher porosity, where air can freely circulate through the material, tend to burn faster due to increased oxygen availability.

Now, let's analyze the given options:

A. A log, two feet in diameter: This log has a large volume and a relatively low surface area compared to the other options. It will burn slower because the oxygen can penetrate the outer layer of the log only, and it takes longer for the combustion to propagate through the entire volume of the log. Therefore, it will burn slower than other options.

B. Two logs, each one foot in diameter: Since these logs are smaller in diameter compared to option A, they have a larger surface area-to-volume ratio. This means they will burn faster than a single log with a larger diameter but slower than the smaller splinters in option C.

C. A pile of small splinters made from a two-foot diameter log: The pile of small splinters has the highest surface area-to-volume ratio among the options. The smaller size increases the exposed surface area, allowing for faster combustion. Oxygen can rapidly access the entire pile, leading to quick and efficient burning. Therefore, the splinters will burn the fastest of the given options.

D. Both logs and the splinters will burn at the same rate. This option is not accurate because, as explained above, the surface area-to-volume ratios differ between the logs and the splinters. Consequently, they will burn at different rates, with the splinters burning the fastest.

In conclusion, the correct answer is C. A pile of small splinters made from a two-foot diameter log, which will burn the fastest in open air due to its high surface area-to-volume ratio.