Question:
If the coefficient of performance of a refrigerator is 5 and operates at the room temperature, find the temperature inside the refrigerator.
Solution:
To find the temperature inside the refrigerator, we need to find the work done
W = 0
Q1 = Q2
β = ∞
Where β is the coefficient of performance
Given,
T1 = 27 + 273 = 300 K
Coefficient of performance of refrigerator ω = 5
Coefficient of performance is given as
$\beta=\frac{Q_{2}}{Q_{1}-Q_{2}}$
Using the above equation, the temperature can be determined
$\omega=\frac{T_{2}}{T_{1}-T_{2}}$
T2 = -23oC.