In the event that MOST of the world population were wiped out in a plague / apocalypse that did not directly destroy infrastructure, just killed the people, how long would infrastructure like the power grid, phone network, internet, gps system continue to run?
Would nuclear power stations meltdown or do they have automated safety shutdowns?
Just to be clear i'm talking about a plague that kills 99.9% of the population of earth, leaving just 6 million people alive spread around the world.
If those 6 Million people can start again with a clean sheet and the technologies of 2016 I would imagine that they could re-build a world that would be OK, but if they are reduced to medieval levels of tech its a tougher place to be...
After one year, typical spent nuclear fuel generates about 10 kW of decay heat per tonne, decreasing to about 1 kW/t after ten years. Hence effective active or passive cooling for spent nuclear fuel is required for a number of years.
If no cooling system is working to remove the decay heat from a crippled and newly shut down reactor, the decay heat may cause the core of the reactor to reach unsafe temperatures within a few hours or days, depending upon the type of core. These extreme temperatures can lead to minor fuel damage (e.g. a few fuel particle failures (0.1 to 0.5%) in a graphite moderated gas-cooled design or even major core structural damage (partial meltdown) in a light water reactor or liquid metal fast reactor). Chemical species released from the damaged core material may lead to further explosive reactions (steam or hydrogen) which may further damage the reactor.
(References have been removed from the quoted texts.)
In short, the reactors will shut down, but if there's no-one left to keep the cooling going properly for long enough, then it's quite likely there will be some serious accidents.
So there's a very good chance that large-scale power generation will be shut down rather quickly, within a few days or weeks. Not necessarily broken and unrepairable, though.