As it takes 3.8 kw to freeze a metric ton (1000 kg) of water ( heat of 
fusion ~ 333 kJ/kg) a day, an ordinary  60 megawatt nuclear submarine 
reactor could at best  create about 16,000 cubic meters of new sea ice .

 So if all  ~ 150 of the world's nuclear submarines  were deployed to the 
Arctic, they might freeze ~ 2.4 square kilometers a day, or 876 square 
kilometeres a year. 
Since summer  sea ice extent has declined roughly 3 million km2 since 1980, 
it would take the existing nuclear submarine fleet more than 3,000 years to 
restore polar albedo to its state in 1980 Or twice that if you throw in 
Antarctic sea ice loss

More nuclear subs could of course do the job in a single generation, but 
that would entail commissioning a fleet of 30,000 SSN's
.Our latest  design ,the Columbia class are expected to cost 12 billion a 
pop, or 5 billion each by the dozen  or but China's yard capable of 
building 4 more modest nuclear attack subs at a time, which in mass 
production might cost a mere few billion each, cutting the cost 
of Kotahatuhaha & Co.'s modest proposal to a scant $100 trillion., plus a 
the discount cost of an order of magnitude uptick in proliferation risks- 
 SSN's run on highly enriched uranium.


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