Question

A manufacturer of ice cream freezers claims that its product has a coefficient of performance of 1.3 while freezing ice cream at 250 K when surrounding environment is at 300 K. Is this claim valid?

Answer 1

The manufacturer's claim of a coefficient of performance of 1.3 for the ice cream freezer is valid.

Step-by-step explanation:

The coefficient of performance (COP) can be calculated using the equation COP = Qc / W, where Qc is the heat transferred from the cold environment and W is the work done by the refrigerator.

In this case, the manufacturer claims that the COP is 1.3.

To determine if this claim is valid, we need to compare the calculated COP with the claimed COP.

Let's calculate the COP:

COP = Qc / W

= (Th - Tc) / W

Given the freezing temperature of ice cream (Tc) as 250 K and the surrounding environment temperature (Th) as 300 K, we can substitute these values into the equation:

COP = (300 K - 250 K) / W

= 50 K / W

= 1.3

To find the validity of the claim, we need to solve for W:

W = 50 K / 1.3 = 38.46 K

Substituting this value back into the equation:

COP = (300 K - 250 K) / 38.46 K

= 50 K / 38.46 K

= 1.3

Since the calculated COP matches the claimed COP, we can conclude that the manufacturer's claim is valid.