The coefficient of performance of a refrigerator is 5. If it is placed in a room at a temperature of 39°C, the temperature inside the refrigerator is:
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The coefficient of performance for refrigerators and heat pumps can be used to determine the temperature inside the appliance, given the room temperature.
The coefficient of performance (COP) for a refrigerator is given by:
\[
COP = \frac{T_2}{T_1 - T_2}
\]
where \(T_1\) is the temperature of the room (in Kelvin) and \(T_2\) is the temperature inside the refrigerator (in Kelvin). Given that \( COP = 5 \) and \( T_1 = 39^\circ C = 312 \, K \), we can solve for \(T_2\) by converting the temperatures into Kelvin.
\[
5 = \frac{T_2}{312 - T_2}
\]
Solving the equation for \(T_2\), we get \(T_2 = 260 \, K\). Converting this back to Celsius:
\[
T_2 = 260 - 273.15 = -13^\circ C
\]
Thus, the temperature inside the refrigerator is \( -13^\circ C \).
