An ideal refrigerator-freezer operates with a COP = 8.0 in a 28°C room. What is the temperature inside the freezer?
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To find the temperature inside the freezer, we need to use the Coefficient of Performance (COP) formula for a refrigerator, which is given by:
COP = Tc / (Th - Tc)
Where:
COP = Coefficient of Performance
Tc = Temperature inside freezer (in Kelvin)
Th = Temperature in the room (in Kelvin)
First, let's convert the room temperature from Celsius to Kelvin:
Th = 28°C + 273.15 = 301.15 K
Next, we can rearrange the formula to solve for Tc:
Tc = COP * (Th - Tc)
Plugging in the given COP value of 8.0, we have:
Tc = 8.0 * (301.15 - Tc)
Simplifying the equation,
Tc = 2409.2 - 8.0Tc
Combining like terms,
9.0Tc = 2409.2
Solving for Tc, we divide both sides by 9.0:
Tc = 2409.2 / 9.0
Calculating the value,
Tc ≈ 267.69 K
Converting back to Celsius,
Tc ≈ 267.69 K - 273.15 = -5.46°C
Therefore, the temperature inside the freezer would be approximately -5.46°C.