dpb writes:
wrote:

certinally coal nuclear and oil fired plants with thoise big cooling
towers waste lots of heat........

I'll wager their overall thermal efficiency is higher than these units.
You can't escape the 2nd law...

A thermal power plant's useful output is electricity only. It's hard to
generate electricity from heat, and a lot of the heat ends up being
dumped by the cooling tower in order to create a larger temperature
differential to boost the efficiency of the turbines.

With a cogeneration unit, the heat output is counted as useful output
instead of waste heat when calculating efficiency. But that's fair only
if you actually need the water heating.

So the cogen unit is almost certainly less efficient at generating
electricity than the large utility unit, if that's the only output you
count. The cogen unit is also probably less efficient at heating water
than a high-efficiency dedicated water heater, if you only measure water
temperature rise as useful output. It's only when you count *both*
water heat and electricity that you end up with the high quoted
efficiency.

Dave