Science Buddies: "Ask an Expert"

Estimate the difference in energy produced when we burn 1kg of carbon vs producing nuclear energy from 1kg of U-235.

C + O2(g) -> CO2(g)

I have this:

U-235

Specific Heat Capacity of Carbon is 0.710 J/kgK
1kg Carbon = 1000kg /12g C/1moleC = 83.26 moles C
Amount of heat released when 1 kg of C is burned:
0.710kJ/mol x 83.26 moles C/1mole C = 59.1146 kJ
1kg of C releases 59.1146 kJ

1 kg Uranium-235 = 0.12 J/kgK = specific heat capacity of U
1 kg Uranium 1000kg/238g U/1mole U = 4.20 moles U
0.12kJ/mol x 4.20 moles U/1mole U = .504 kJ
1kg of U releases .504 kJ

U235 + n --> fission + 2 or 3 n + 200 MeV
1MeV (million electron volts) = 1.609 x 10^-13 j this corresponds to 3.2 x 10^-11 j

4.20 moles CO2 x 6.022x10^23 molecules/1mole CO2 molecules = 2.52x10^24


3.2x10^-11 J / 2.52x10^24 J = 1.269x10^13
The fission process releases over 12 trillion times more energy per kg of fuel.


My teacher said that I did something wrong here (J/mol conversion for Carbon and Uranium235) also I have the wrong value for 1kg of U since it releases more heat than 0.504kJ. Then recalculate. I need help very very detailed step by step help. PLEASE!

Hi quantum! Welcome to the Forum.

This Forum is for help with Science Fairs. Your question looks more like a homework problem than a Science Fair issue. But nonetheless I have a few of things to say about your calculations. First, the abbreviated presentation is VERY CONFUSING, especially where mol seems to stand for molecule in one spot and mole (which is correct) in another. Second, the specific heat capacity has nothing to do with the amount of energy released when carbon is burned or when uranium is fissioned. Third, the line

3.2x10^-11 J / 2.52x10^24 J = 1.269x10^13

is obviously incorrect. Fourth, one of the starting points of your calculations (first line) includes the unit kelvin, symbol K; where does it go, since it does not show up in the output number? Finally, when writing calculations such as yours, be sure to state abbreviated units with correct spaces in their names. For example

J/kgK

should be written as either

J/(kg K) or J kg^-1 K^-1

where the former looks better in an email written in plain text, and the latter, in formatted text such as produced by most text writing software or used in html. When, in particular, K for kelvin is used, there is the danger of confusion with k, as in kJ or KJ, or with k, Bolzmann's constant.

Good luck!