Energy Saving Calculation During Mild Weather

(when the outdoor is colder than the kitchen)


Below calculations are based on reverse Carnot cycle (not the vapor compression cycle).  The vapor compression cycle is the one used in the actual refrigerators.  The reverse Carnot cycle is a hypothetical cycle that real devices don't use.  For more accurate vapor compression cycle please see the notes of Mr. Pei-feng Hsu, Ph.D. Professor & Department Head Mechanical & Aerospace Engineering Department of Florida Inst. of Technology.  


The following energy saving calculation and the resulting formula: H = (C - B) / (C - D) have also been reviewed and verified by a third party expert. The resulting formula is used in a Spreadsheet to show the energy saving rate based on different indoor and outdoor temperatures.


For an accurate comparison, it is assumed that both refrigerators/freezers (R/Fs) have the exact same power, motor, compressor, cubic volume, and component efficiencies. All external environmental variables are likewise assumed to be the same, such as the inside temperature of the R/Fs, the room temperature, the type and amount of refrigerant, the number of times the R/Fs' doors are opened and closed, etc. Therefore all functional inefficiencies occur equally on both sides of the equation and cancel each other out and have no impact on the results of the calculations.


Basic math skills is the only requirement to understand the following calculations. 


Wi = Work or electricity consumption of the Indoor R/F.

Ww = Work or electricity consumption of the Window R/F.


Qi = Heat absorbed by the evaporator of the Indoor R/F.

Qw = Heat absorbed by the evaporator of the Window R/F.

Qw = Qi  Since both R/Fs are identical - else comparison would be partial.


Ti = temperature difference between Indoor R/F's condenser and evaporator.

Tw = temperature difference between Window R/F's condenser and evaporator.


H = The Energy (electricity) Savings %  =  1- (Ww / Wi)


COP = Q / W (or W = Q / COP). The higher the COP the better, because more heat can be transferred with less work (electricity).  The COP depends primarily on the temperature of the evaporator and the condenser. The closer the two temperatures, the higher the COP. 


Ww / Wi =  (Qw/COPw) / (Qi/COPi)   Since QiQw  Therefore Ww / Wi = COPi / COPw   


COP = cold temperature (Tc) or the temperature of the evaporator, divided by the temperature difference between the evaporator and the condenser (Td).

       COP  <=  Tc / Td    


The real COP will be considerably less than  Tc / Td  depending on the model of the compressor, the type of refrigerant and other variables (which for accurate comparison, we have assumed are exactly the same for both R/Fs (Indoor and Window)).  To simplify let's assume (for both R/Fs) the Real COP =  0.5 x Tc / Td


Now going back to our original table column definitions:


B = Outdoor Temperature = the temperature of Window R/F's condenser.

C = Indoor Temperature = the temperature of Indoor R/F's condenser.

D = The temperature of Indoor and Window R/F's evaporator. 

Ti = C - D = Temperature difference between the Indoor R/F's evaporator and condenser.

Tw = B - D = Temperature difference between the Window R/F's evaporator and condenser.


Substituting these variables in our formula, we get:


COPi =  0.5 x D / Ti     and     COPw =  0.5 x D / Tw   


Or alternatively: 


Ww / WiCOPi / COPw = (0.5 x D / Ti) / ( 0.5 x D / Tw) =  TwTi 


H = % Energy Savings = 1 - (Ww / Wi) = 1 - (TwTi) = (Ti - Tw) / Ti((C - D) - (B - D)) / (C - D)
H =  
(C - B) / (C - D)  
All temperatures must be in Kelvin. However temperature differences (C-B) and (C-D) can be in Celsius because one Celsius is equal to one Kelvin.