Carnot Fridge

#602 / Thermo Easy

Consider a Carnot refrigerator operates between -30°F on the cold side and 120°F on the hot side. What is the max theoretical efficiency?

Expand Hint

For a Carnot refrigeration cycle, the Coefficient of Performance (COP) is:

$$$COP_c=\frac{T_L}{(T_H-T_L)}$$$

where $$T_H$$ and $$T_L$$ are the absolute high and low temperatures respectively in either Kelvin or Rankine.

Hint 2

To convert from Fahrenheit to Rankine:

$$$^{\circ}R\:=\:^{\circ}F+459.69$$$

For a Carnot refrigeration cycle, the Coefficient of Performance (COP) is:

$$$COP_c=\frac{T_L}{(T_H-T_L)}$$$

where $$T_H$$ and $$T_L$$ are the absolute high and low temperatures respectively in either Kelvin or Rankine. To convert from Fahrenheit to Rankine:

$$$^{\circ}R\:=\:^{\circ}F+459.69$$$

Thus, the high and low temperatures are:

$$$^{\circ}R_H=120^{\circ}F+459.69=579.69^{\circ}R$$$

$$$^{\circ}R_L=-30^{\circ}F+459.69=429.69^{\circ}R$$$

Therefore,

$$$COP_c=\frac{429.69^{\circ}R}{(579.69^{\circ}R-429.69^{\circ}R)}=\frac{429.69}{150}=2.86$$$

2.86

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