[TriLUG] OT: thermodynamics of A/C question

[Joseph Mack NA3T]

Summer is no fun here with the heat. The cost of A/C cooling 
is more than for heating in the winter. This lead me to 
wonder if there is any way around the cost of A/C?

For the last month or so, with cool nights, I've had windows 
open with fans blowing the cool outside night air in through 
the open windows. Until a couple of days ago, the house was 
in the 60's in the morning and stayed about 10degF below the 
outside temp during the day, which was quite accepable.

Then yesterday, with the night not being cool anymore, I had 
to turn on the A/C. It occured to me that I should run the 
A/C at night, when the air outside was cooler, instead of 
runing it during the day. If I'm trying to remove a certain 
fixed number of BTUs, I expect the A/C works better, from a 
Carnot cycle point of view, if the heat sink is cooler.

Let's say I want the house temp to not go above 82degF 
during the day (and don't care how cold it is at night).

I can either

o set the A/C to 82degF and have it run during the day 
dumping to air at 90degF (say). Then at night the A/C 
doesn't run much (at least in the current weather). In the 
morning, the house is still 82degF.

o set the A/C to 76degF when I go to bed. I wake up to a 
cold house in the morning and set the A/C back to 82. The 
A/C doesn't run during the day (at least for today, with 
90degF outside).

from

https://en.wikipedia.org/wiki/Carnot_cycle#Efficiency_of_real_heat_engines

Carnot efficiency = 1-Tc/Th

My head hurts trying to think about Carnot cycles at the 
interface between the high pressure exchanger (compressor) 
and the outside air on one hand, and the low pressure 
exchanger (evaporator) and the inside air on the other hand. 
I assume for my scenario, the only change to be considered 
is at the compressor exchanger, which is dumping to outside 
air, ie only the outside air temperature changes much. The 
compressor exchanger is hot (too hot to touch) which puts it 
at 160degF or so (the temperature of hot domestic hot water) 
=60degC=330degK.

Lets assume that the outside day temp is 310degK and the 
outside night temp is 300degK.

The efficiency changes from

1-310/330=6% to 1-300/330=9%, ie an increase in efficiency 
of 50%.

Now I know that the heat exchangers in an A/C aren't Carnot 
cycle, but I don't know how else to model them.

This article models an A/C as a Carnot cycle machine

https://en.wikipedia.org/wiki/Seasonal_energy_efficiency_ratio

but the equation presented

https://en.wikipedia.org/wiki/Seasonal_energy_efficiency_ratio#Theoretical_maximum

has a singularity at Tc=Th. Clearly an A/C still works if 
the inside and outside temperature is the same.

Got any idea, if I want to remove a fixed number of BTUs, 
whether running the A/C at night is any better than during 
the day, or am I having myself on?

Thanks
Joe

-- 
Joseph Mack NA3T EME(B,D), FM05lw North Carolina
jmack (at) wm7d (dot) net - azimuthal equidistant map
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