Consider a power station set up in the middle of a town with cold winters. In the first example it burns has, drives a turbine and cycles water back after some form of basic cooling loop.
In the second example the waste heat (after driving the turbine) is connected to a distributed heating system throughtout the town that heats buildings and pavements and so on. In this case the return loop is much lower temperature, say just above freezing.
In order to do work you need a temperature gradient, although I’m not sure if that is relevant here. On the one had there will be a bigger gradient between the boiled and cooled water, but on the other hand you need to use more energy to lift the temperature from the cooling loop to boiling.
How does the efficiency for purely energy generation compare in these cases?
No, return loop temp can never be colder than what cools it…
So unless your building is below freezing, the return loop won’t be freezing.
Which is a good thing, because even almost frozen water has exceptionally poor flow rate.
Like, you’re completely ignoring why a secondary loop is required, but even accounting for that it’s just not a huge gain. Obviously you’d have primarycoming out at its hottest and heating the secondary after it’s went thru whatever loop, but you’ll still need to add extra heat unless it’s an incredibly tiny and nearby secondary loop.
That’s why most building that have their own boiler for energy used potable water heating and never really scaled up to heating buildings or melting sidewalks in the winter. Like, you’d only need that 3-6 months a year, it would take forever to recoup the cost of install. Most likely you wouldn’t.
Every building with a boiler always needs hot water tho…