Using Isothermally Compressed Air to Cool a Refrigerator

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To calculate the amount of isothermally compressed air needed to maintain the temperature of a 14 cf refrigerator at 3 degrees C and an 18 cf freezer at -18 degrees C, one must first determine the final temperature of the air after adiabatic and reversible expansion from 7 psig to 0 psig. This involves applying thermodynamic principles to find the temperature drop during expansion. Once the final temperature is established, the heat transfer required to maintain the desired temperatures in the refrigerator and freezer can be calculated. The volume of air needed per unit time can then be derived from these calculations. Accurate calculations will ensure efficient temperature maintenance in both appliances.
Andy049
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If I have a steady supply of isothermally compressed air at 7 psi (approximately 148 kPa) at a temperature of 4 degrees C, how would I calculate the amount needed of that air per unit time to maintain the temperature of a 14 cf refrigerator at 3 degrees C? A 18 cf freezer at -18 degrees C?
 
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The first step would be to determine the temperature that the air would attain if it were expanded adiabatically and reversibly from a pressure of 7 psig to a pressure of 0 psig.
 

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