Perhaps my understanding is wrong but I usually think about this in
the following way:

To get net heat flow of Pf from source at temperature T0 to sink at
temperature T1 requires power P1.

If T0>T1, the heat flow is spontaneous, P1 is negative, and you can
actually get some useful work out of the system by using a heat
engine.

If T0<T1, then you need to input a positive P1 power in order to
"pump" the heat against the temperature gradient. However, the power
P1 which you input to the system also gets converted to heat and
contributes to Pf. So, you actually get Pf+P1 heat flow out into the
sink at temperature T1.

If you are going to heat a house using electricity, you could use a
pure resistive heater and be 100% efficient (i.e., all of your input
power is converted to heat). You could alternatively use a heat pump,
in which case you input P1, which allows you to push Pf heat flow
against the gradient from the cold outside to the warm inside, so the
total thermal input power to the house is Pf+P1. There is still strict
conservation of energy because Pf came from heat taken from outside,
it didn't just appear from nowhere. The air outside got colder when Pf
was taken from it.

It also isn't a violation of thermodynamics because the heat didn't
flow against the gradient spontaneously - power P1 had to be input to
cause the reverse heat flow.

It's the same thing as saying that an air conditioner heat sink must
dissipate the sum of the electrical input power AND the heat flow from
the cold side. But we have turned the air conditioner unit around so
that we are cooling the outside and heating the inside. In both cases
we are moving heat against the temp gradient.

Sean


On Sat, Nov 6, 2010 at 10:26 AM, Olin Lathrop <olin_piclist@embedinc.com> w=
rote:
> RussellMc wrote:
>> 4. Deciding whether efficiency can be > 100% requires you to define
>> efficiency in advance.
>> Heat pumps can in fact deliver a net gain in available energy wrt
>> energy in. This is NOT simply a "steal it from somewhere else and its
>> zero sum all round" - it's a real gain - BUT does not break the laws
>> of physics (as ye canna). It works by piling spare heat energy on top
>> of existing heat energy rather than creating it from another form of
>> energy, as is normally done.
>
> This is correct but to clarify for others, the reason the "free" heat isn=
't
> really a violation of physics is because the same gain you got to make th=
e
> heat cheaply works backwards if you then want to convert that heat to any
> other form of energy.
>
>
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