Carnot Fridge
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
Time Analysis
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