# Hypothetical question

1. Jun 28, 2009

### redsrtturbo

I haven't found an answer to this and I can't go to sleep until I do-

If two refrigerators are at the same thermostat setting. One empty (assumed regular Earth air inside) and one full of food.

Both have already reached the temperature on the thermostat. Which will require more energy to maintain at the set temperature (not specified)?

I don't know what equations to use here or if my thoughts are even in the right direction but here goes:

It would take more energy to maintain the fridge full of food b/c it has more matter that is subject to reaching equilibrium and so the refrigerator has to actively fight this and costs more energy than the fridge full of air.

Hit or Miss?

Last edited: Jun 29, 2009
2. Jun 29, 2009

### Bob S

The only heat leak in a cold refrigerator is the thermal conductance in the refigerator walls, assuming the door seals well. It requires electrical energy to keep the inside cold. The average power W (watts) to keep it cold is W = C*(room temp-inside temp), where C = conductance. This does not depend on whether there is any food in it, as long as the food is cold. A refrigerator full of food will stay colder longer than one that is empty when there is a power failure, but it will take longer to cool it down again when the power comes back on.

3. Jun 29, 2009

### Naty1

As usual, Bob S is right on: heat gain and loss in general is via conduction, convection and radiation.

You have the right idea insofar as it likely takes more energy for the initial cooling; once all contents are at equilibrium it's equal with the door kept closed.

With a refrigerator, heat gain or loss is proportional to the temperature difference between inside and outside, as he notes. I monitor this closely on my boat because I use 12 volt dc batteries and a 12volt refrigeration compressor. (This redcues my need to run a relatively expensive diesel generator just for refrigeration.) If the internal frig temp is, say, 40 degrees and the ambient room temperature is say 65 degrees thats a 25 degree temperature. So if the room temperature is instead 90 degrees,as on a really hot summer day, that's 50 degrees above the refrig temp: so my batteries have to supply about twice the power. I can tell the difference just from the extra time the compressor runs and the extra time to recharge batteries when I do run a generator.

BUT, in practical use, a full frig, once fully cooled, takes less power to keep at that temperature because when the door is opened, less cold air escapes and has to be recooled. The contents "holds" cold better since cold it leaks out an open door much more slowly. Besides, selections for dinner are more varied!

4. Jun 29, 2009

### Bob S

Good point. An empty 20 cubic foot refrigerator holds about 0.54 cubic meters (750 grams) of cold air. It spills out and onto the floor every time we open the 'frig'.
Bob S