# Turning Nuclear Weapons into Nuclear Power

## Introduction

 Fig. 1: Energy of various nuclear weapons in the US nuclear arsenal. (See also Table 1. Source: N. Martelaro after Kristensen and Norris. [1])

1. How much energy can we get from nuclear weapons?

2. What can one do with this amount energy?

## Energy Calculation

The energy contained in bombs is listed in tonnes of TNT. This is an energy measurment and is equal to 4.2 × 109 J. For our calculations, we will assume that all the energy in a bomb can be converted to into usable heat energy. We will then assume that about 2/3 of this heat energy is turned into electricity in the plant's steam turbines. With this energy, we can then calculate how long it might power a city. In this case, we use Los Angeles, CA, USA as an example city. The 5-county Los Angeles metropolitan area uses on average 1.4 × 1010 W.

As short example, we convert the energy of the Fat Man bomb dropped on Nagasaki. Fat Man was rated at 20 kT (kilotonne TNT). Converting this energy to joules, we obtain

20 × 1000 × 4.2 ×109 J = 8.4 × 1013 J

The corresponding amount of electric energy is 2/3 of this heat energy, or 5.5 × 1013 J. This amount of energy could power the Los Angeles metropolitan area for

5.5 × 1013 J / ( 1.4 × 1010 J/sec × 3600 sec/hour) = 1.1 hours.

While this may not seem that long, it is interesting to consider that a city uses the same amount of energy in two hours as it would take to destroy it. We can also consider the cost of this energy as another benchmark of the value in the bomb. Nuclear energy costs (estimated for 2022 and without government subsidies) about 10 cents per kilowatt hour to produce, giving [6]

1.4 × 1010 W × 0.001 kWh/Wh × 1.1 h × \$0.1/kWh = \$1,540,000

With these energy conversions we can estimate how much energy and how useful the energy may be for the current US nuclear deployment. There are currently about 2000 nuclear weapons deployed in the US arsenal, spread across various types weapons. Table 1 shows the total amount of energy that each class of nuclear weapon would yield and the total amount of time this energy could power Los Angeles. [1]

Weapon Class Warhead Quantity Yield per
[kT]
Number of
Electrical Energy [J] LA Power [days] Notes
Mk-12A W78 200 335 1 1.86×1017 153
Mk-21/SERV W87 250 300 1 2.81×1017 171
Mk-4 W76 168 100 4 1.86×1017 154
Mk-4A W76-1 600 100 4 6.65×1017 550
Mk-5 W88 384 455 4 1.94×1018 1601
B-52H Stratofortress ALCM
W80-1
200 77.5 1 4.3×1016 171 Average yield. Range: 5 - 150 kT
B-2A Spirit B61-7, -11
B83-1
100 750 1 2.08×1017 171 Average yield. Max: 1200 kT.
B61-3, -4 B61-3, -4 180 85 1 4.25×1016 35 Average yield
Total 2082 2202 3.48×1018 2873 7.8 years
Table 1: Energy estimate of the current US nuclear arsenal. [1]

We see that the currently deployed US nuclear aresenal has a combined total of roughly 5.27 × 1018 J of energy. Converted at 66% efficiency to electricity, this gives 3.84 ×1018 J - enough to power Los Angeles for roughly 7.8 years. It should be noted that this calculation only includes the currently deployed arsenal. There are still another ~2000 warheads kept as spares and another ~2000 awaiting disarmament. [1] Thus, this estimate is most likely a lower bound on the total amount of energy that can be reclaimed from the US nuclear arsenal.

© Nikolas Martelaro. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] H. M. Kristensen and R. S. Norris, "US Nuclear Forces, 2015," Bull. At. Sci. 71, 107 (2015).

[2] C. DiOrio, "The Megatons to Megawatts Program," Physics 241, Stanford University, Winter 2016.

[3] B. Madres, "Market Justifiable Nuclear Energy," Physics 241, Stanford University, Winter 2011.

[4] T. Strobel, "Demilitarization of Nuclear Weapons," Physics 241, Stanford University, Winter 2016.

[5] G. Brumfiel, "Megatons To Megawatts: Russian Warheads Fuel U.S. Power Plants," NPR, 11 Dec 13.

[6] "Annual Energy Outlook 2016," U.S. Energy Information Administration, DOE/EIA-0383(2016), August 2016.