ini kelanjutan lagi dari artikel aslinya.
n the conversion of moles to kilograms we have assumed the atomic weights of hydrogen, carbon, nitrogen and oxygen are 1, 12, 14 and 16 respectively.
Now each of the towers contained 96,000 (short) tons of steel. That is an average of 96,000/117 = 820 tons per floor. Lets suppose that the bottom floors contained roughly twice the amount of steel of the upper floors (since the lower floors had to carry more weight). So we estimate that the lower floors contained about 1,100 tons of steel and the upper floors about 550 tons = 550 x 907.2 ≈ 500,000 kgs. We will assume that the floors hit by the aircraft contained the lower estimate of 500,000 kgs of steel. This generously underestimates the quantity of steel in these floors, and once again leads to a higher estimate of the maximum temperature.
Each story had a floor slab and a ceiling slab. These slabs were 207 feet wide, 207 feet deep and 4 (in parts 5) inches thick and were constructed from lightweight concrete. So each slab contained 207 x 207 x 1/3 = 14,283 cubic feet of concrete. Now a cubic foot of lightweight concrete weighs about 50kg, hence each slab weighed 714,150 ≈ 700,000 kgs. Together, the floor and ceiling slabs weighed some 1,400,000 kgs.
So, now we take all the ingredients and estimate a maximum temperature to which they could have been heated by 3,500 gallons of jet fuel. We will call this maximum temperature T. Since the calorific value of jet fuel is 44 MJ/kg. We know that 3,500 gallons = 31,000 kgs of jet fuel
will release 10,850 x 44,000,000 = 477,400,000,000 Joules of energy.
This is the total quantity of energy available to heat the ingredients to the temperature T. But what is the temperature T? To find out, we first have to calculate the amount of energy absorbed by each of the ingredients.
That is, we need to calculate the energy needed to raise:
39,857 kilograms of water vapor to the temperature T° C,
97,429 kilograms of carbon dioxide to the temperature T° C,
349,680 kilograms of nitrogen to the temperature T° C,
500,000 kilograms of steel to the temperature T° C,
1,400,000 kilograms of concrete to the temperature T° C.
To calculate the energy needed to heat the above quantities, we need their specific heats. The specific heat of a substance is the amount of energy needed to raise one kilogram of the substance by one degree centigrade.
Substance Specific Heat [J/kg*C]
Water Vapor 1,690
Carbon Dioxide 845
Lightweight Concrete 800
Substituting these values into the above, we obtain:
39,857 x 1,690 x (T - 25) Joules are needed to heat the water vapor from 25° to T° C,
97,429 x 845 x (T - 25) Joules are needed to heat the carbon dioxide from 25° to T° C,
349,680 x 1,038 x (T - 25) Joules are needed to heat the nitrogen from 25° to T° C,
500,000 x 450 x (T - 25) Joules are needed to heat the steel from 25° to T° C,
1,400,000 x 800 x (T - 25) Joules are needed to heat the concrete from 25° to T° C.
The assumption that the specific heats are constant over the temperature range 25° - T° C, is a good approximation if T turns out to be relatively small (as it does). For larger values of T this assumption once again leads to a higher maximum temperature (as the specific heat for these substances increases with temperature). We have assumed the initial temperature of the surroundings to be 25° C. The quantity, (T - 25)° C, is the temperature rise.
So the amount of energy needed to raise one floor to the temperature T° C is
= (39,857 x 1,690 + 97,429 x 845 + 349,680 x 1,038 + 500,000 x 450 + 1,400,000 x 800) x (T - 25)
= (67,358,330 + 82,327,505 + 362,967,840 + 225,000,000 + 1,120,000,000) x (T - 25) Joules
= 1,857,653,675 x (T - 25) Joules.
Since the amount of energy available to heat this floor is 477,400,000,000 Joules, we have that
1,857,653,675 x (T - 25) = 477,400,000,000
1,857,653,675 x T - 46,441,341,875 = 477,400,000,000
Therefore T = (477,400,000,000 + 46,441,341,875)/1,857,653,675 = 282° C (540° F).
So, the jet fuel could (at the very most) have only added T - 25 = 282 - 25 = 257° C (495° F) to the temperature of the typical office fire that developed.