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re: solar power efficiency
23 jun 1997
steve willey   wrote:

>i have read that a gas water heater is about 60% efficient...

sounds reasonable, ie the amount of heat energy that goes into the water
is 60% of the amount of heat energy released when the gas is burned. some
gas furnaces are over 90% efficient, but they are larger and may be more
carefully designed.

a "60% efficient gas water heater" might burn a therm of gas "containing"
100,000 btu of heat energy to raise the temperature of 0.60x1,000lb/8
= 75 gallons of water 100 degrees f. "containing," because one standard
definition of gas heater efficiency includes the latent heat of water
in the gas combustion products and one does not. (i think this came about
when more efficient european heaters started condensing water vapor out of
the exhaust gases, and manufacturers wanted credit for that, ie wanted
everyone else's efficiency rating to go down, vs having their heaters show up
"110% efficient" under the old system.) defining "efficiency" can be slippery,
even when people are honest and have no axes to grind, because we need to
define an input, an output, and an ideal (100% efficient) comparison system
and those references are often unstated, which leads to confusion.

we also seem to be mostly talking about "instantaneous efficiency" in the
case of water heaters, ie the energy needed to initially heat the water,
which has little to do with how much insulation surrounds the water heater
(since the water heating happens quickly), vs something that might be called
"storage efficiency" ie the energy needed to keep the water hot for a day
or a month, which depends more on the insulation, or a "working efficiency,"
that might include both heating and storage.

>whereas if that gas was burned in a power plant at 80% efficiency...

if you mean "the amount of electrical energy that the gas produces is 80%
of the amount of heat energy released when the gas is burned," ie that a
therm of gas would produce 0.80x100,000/3410 = 23.5 kwh, i don't think it's
that high. the "boiler efficiency" might be 90%, ie the amount of heat energy
that goes into the steam divided by the amount of heat energy released when the
gas is burned, but we need to multiply that by the thermodynamic efficiency of
converting the heat in the steam into motion, eg btu into horsepower-hours,
which might be closer to 40%, and the mechanical efficiency of converting
the motion into electrical energy, eg horsepower-hours into kilowatt hours, 
which might be close to 90%, with appropriate unit conversions.  

>and transported through lines at 80% efficiency

that transmission efficiency (kwh received at your house divided by kwh
generated at a power plant) might be higher, closer to 90%, depending on
how far you live from the power plant. a power transformer might be 95%
efficient, ie electrical output power/electrical input power = 0.90%. the
wires in a typical power transmission system might be 94% efficient, ie the
electrical power that comes out of the wires might be 94% of the power that
goes in, with the remainder (i^2r), mostly heating the air along the wires,
leaving as static discharges, magnetic fields, etc.

>to an electric water heater at 90% efficiency,

this final efficiency has somewhat ironically and unfortunately come to be
known as "over-all electrical efficiency, the ratio of the power absorbed by
the load material to the total power drawn from the supply lines," ie the
electrical power input (from the new ieee standard dictionary of electrical
and electronics terms, fifth edition, 1993, published by the largest
engineering organization in the world, the institute of electrical and
electronics engineers.) even this standard dictionary definition is slightly
ambiguous, because it doesn't say where the input power is measured. at the
water heater, at the fusebox, at the utility pole? most people would say 
"at the water heater."

we can't change the way most people use this word in this case, at least
not quickly, no matter how much we like renewable energy. we might just change
the way we use the word, but to me that somehow seems dishonest, or at least
confusing, perverse, and uncooperative. (can you imagine going through life
consciously or unconsciously but consistently using the word "red" for what
the rest of the world calls "green"? our friends would catch on eventually,
but most people would consider that very odd.) 

>it takes more gas at the power plant to heat the water for the same shower.

let's see: as our reference, an "ideal 100% efficient system" might use
10x3x8x(110-60) = 12,000 btu to heat water for a 10 minute 3 gpm shower from
60 to 110 f. an "80% efficient gas water heater" needs 12k/0.80 = 15,000 btu
of "gas energy" to do this job. a "99% efficient electric water heater" needs
12k/0.99 = 12,121 btu of electrical energy to do this job, which might require
a whopping 12,121/(0.94x0.95x0.95x0.90x0.40x0.90) = 44,098 btu, after losses
owing to the efficiency of high voltage transmission wires, the efficiencies
of a couple of transformers, the mechanical efficiency of an alternator, the
thermodynamic efficiency of a turbine, and the boiler efficiency of burning
gas to produce steam. 

>then there is economics...

right. that has nothing to do with this kind of technical energy efficiency,
in my book. although economists speak of "efficient markets," bureaucrats
speak of "efficient offices" and sports people speak of "efficient tennis
players." how do we define the efficiency of a bicycle or a clothesline?  


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