Question

In a mechanical refrigerator, the low temperature coils are at a temperature of $-{23}^{o}C$ and the compressed gas in the condenser has a temperature of ${27}^{o}C$. What is the theoretical coefficient of performance?

Answer 1

Step 1: Given data

The temperature of the condenser,

$$\begin{gathered} Kelvin=Celsius+273 \\ {T}_1=27+273[As{T}_{1}ishigherthan{T}_2] \\ {T}_1=300k \end{gathered}$$

Temperature of the coil,

$$\begin{gathered} T_{2}inkelvin=Celsius+273 \\ {T}_2=-23+273 \\ {T}_2=250k \end{gathered}$$

Step 2: The coefficient of performance

1. The Coefficient of Performance, or COP, is a ratio of useful heating or cooling to the amount of effort required in a system.
2. Higher COPs are likely to lower operating costs.
3. The COP usually exceeds one, especially in heat pumps, because instead of merely converting work to heat, which would have a COP of one if it were 100 percent successful, it pumps extra heat from a heat source to where the energy is required.

Step 3: Formula used

$Coefficientofperformance=\frac{Output}{Input}=\frac{T_2}{T_1-T_2}$

Step3: Calculating coefficient of performance

$$\begin{gathered} Coefficientofperformance=\frac{T_2}{T_1-T_2} \\ Coefficientofperformance=\frac{250}{300-250} \\ Coefficientofperformance=5 \end{gathered}$$

Hence, the theoretical coefficient of performance is $5$.