I have some issues with your numbers. (I hope you still read this thread a day later.)
First where I live water is about 4-10 degree C, not 20. So that bumps your water heating energy (assuming your 1/4 liter volume is correct) to 43kJ. But washing dishes uses about 20 gallons per sinkful. Say a sink can hold 8 bottles, that means you need about 9 liters of water per bottle to wash it - not a 1/4 liter. (A dishwasher is much more efficient BTW.)
So 43kJ * 36 = 1548kJ.
At 150 degrees a 1 liter bottle needs 2.6 grams of steam to fill it. (Density from http://www.engineeringtoolbox.com/saturated-steam-properties... at temperature of 150.) And using my number of 4 degrees for incoming water, your energy use is 2261 kj/kg * 2.6 grams = 5.88kJ.
So your total is 1548kJ + 5.8kJ + 22kJ = 1576kJ vs 200kJ. i.e. it's not even close.
A dishwasher uses 4 gallons per load, and you can fit about 20 bottles in there. Which is .75l per bottle - way better than by hand. Using those numbers your total is 157kJ per bottle compared to 200kJ.
So it's ever so slightly better - but of course we are ignoring transportation and sorting costs. Not to mention the factory for sterilizing bottles. (You anyway need one to make glass and bottles, to reuse them you must build a whole new factory.)
And the real kicker is the extra water. Currently the world has enough energy, but not enough water. (Maybe we should calculate desalination costs for the water and bundle it into the energy budget.)
Where I live the temperature of the water is about the same as the temperature of the air, which typically varies between -10° and 40° in human-inhabited zones. But the main point here is really that what matters is how you wash the bottles: if you wash them in running hot water, which I think is what you're talking about when you say "20 gallons per sinkful", then you get megajoule-scale numbers. If you wash multiple sinkfuls of dishes with a sinkful of dishwater, you get a number lower by a factor of 20, like I did. And if you wash your bottles in cold water, you get even lower numbers.
In my previous comment I was tempted to suggest washing in salt water, but ① very few people do that, and ② it's a pain, because the salt makes the soap stop working.
Desalination turns out to be a reasonable cost, but still one that tips the balance in favor of recycling rather than reuse. Typical desalination plant costs are half for energy and half other things (like plant construction), and total about US$0.001 per liter. If we assume that all, rather than half, of that cost pays for energy, and at the typical wholesale price of US$40 / megawatt-hour, it works out to 95kJ/liter. So the answer still depends on factors like how cold your water is before it goes into the hot water heater, how much water you use per bottle, and stuff like that.
I don't agree about your factory construction line item; if you reduce the demand for glass bottles by reusing old ones instead of melting them down, you need fewer bottle factories.
> Where I live the temperature of the water is about the same as the temperature of the air
How do you manage that? By me the water comes in from underground pipes and is always the temperature of the ground, which stays pretty constant (and cold) year round.
> suggest washing in salt water
And aside from the other things you mentioned, most people don't have access to salt water. In the US it's only available on the coasts, but the coasts are usually premium land and not available for industry.
I do think we've basically come to an agreement that it depends mainly on the process used for washing the bottle.
With two points of disagreement: I still think the extra labor needed tips the energy balance away from reuse. And I think that trading water for energy is worth it.
> reduce the demand ... you need fewer bottle factories.
It's much easier to make a factory larger than it is to build a whole new one.
First where I live water is about 4-10 degree C, not 20. So that bumps your water heating energy (assuming your 1/4 liter volume is correct) to 43kJ. But washing dishes uses about 20 gallons per sinkful. Say a sink can hold 8 bottles, that means you need about 9 liters of water per bottle to wash it - not a 1/4 liter. (A dishwasher is much more efficient BTW.)
So 43kJ * 36 = 1548kJ.
At 150 degrees a 1 liter bottle needs 2.6 grams of steam to fill it. (Density from http://www.engineeringtoolbox.com/saturated-steam-properties... at temperature of 150.) And using my number of 4 degrees for incoming water, your energy use is 2261 kj/kg * 2.6 grams = 5.88kJ.
So your total is 1548kJ + 5.8kJ + 22kJ = 1576kJ vs 200kJ. i.e. it's not even close.
A dishwasher uses 4 gallons per load, and you can fit about 20 bottles in there. Which is .75l per bottle - way better than by hand. Using those numbers your total is 157kJ per bottle compared to 200kJ.
So it's ever so slightly better - but of course we are ignoring transportation and sorting costs. Not to mention the factory for sterilizing bottles. (You anyway need one to make glass and bottles, to reuse them you must build a whole new factory.)
And the real kicker is the extra water. Currently the world has enough energy, but not enough water. (Maybe we should calculate desalination costs for the water and bundle it into the energy budget.)