Question

If a refrigerator of coefficient of performance (COP) 5 has a freezer at a temperature of -13 °C, then the room temperature is

• A. 325 °C
• B. 225 °C
• C. 39 °C
• D. 29 °C

Hint:

Always convert temperatures to Kelvin when using thermodynamic formulas for COP.

Answer 1

The Correct Option is C

Step 1: Use the formula for COP of refrigerator
\[ COP = \frac{T_c}{T_h - T_c} \] where \(T_c\) = cold temperature (freezer), \(T_h\) = hot temperature (room), in Kelvin.
Step 2: Convert temperatures to Kelvin
\[ T_c = -13 + 273 = 260\, K, \] \(COP = 5.\)
Step 3: Calculate \(T_h\)
\[ 5 = \frac{260}{T_h - 260} \implies 5(T_h - 260) = 260 \implies 5T_h - 1300 = 260 \implies 5T_h = 1560 \implies T_h = 312\, K. \] Step 4: Convert back to °C
\[ T_h = 312 - 273 = 39^\circ C. \] Step 5: Conclusion
Room temperature is 39 °C.