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A 1 m by 1 m by 2 m freezer has 10 cm thick foam walls (k=0.04Wm−1 K−1). You must keep the interior at −5 ∘C in a 20 ∘C room with a COP 3.5 cooling system. Assume heat is lost through all six (6) sides of the freezer. What is the electrical power required to run the freezer for 1 hour?

User CRUTER
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Final answer:

To calculate the electrical power required to run the freezer for 1 hour, we need to determine the amount of heat that needs to be extracted from the freezer interior. The heat transfer rate through the foam walls can be calculated using the formula Q = k * A * (ΔT / d). The electrical power required is given by Power = COP * Q.

Step-by-step explanation:

To calculate the electrical power required to run the freezer for 1 hour, we need to first determine the amount of heat that needs to be extracted from the freezer interior. The volume of the freezer is 1 m x 1 m x 2 m = 2 m³. The heat transfer rate through the foam walls can be calculated using the formula:

Q = k * A * (ΔT / d)

Where Q is the heat transfer rate, k is the thermal conductivity of the foam, A is the surface area of the freezer, ΔT is the temperature difference between the interior and the room, and d is the thickness of the foam walls.

The surface area of the freezer is 6 m² (2 sides * 1 m x 1 m, 2 sides * 1 m x 2 m, and 2 sides * 1 m x 1 m), the temperature difference is 20 °C (20 °C - (-5 °C) = 25 °C), and the thickness of the foam walls is 0.10 m (10 cm = 0.10 m).

Plugging in these values, we get:

Q = 0.04 W/m·K * 6 m² * (25 °C / 0.10 m) = 600 W

This is the heat that needs to be extracted from the freezer interior every second. To find the electrical power required, we can use the equation:

Power = COP * Q

Where COP is the coefficient of performance of the cooling system. In this case, COP = 3.5.

Plugging in the values, we get:

Power = 3.5 * 600 W = 2100 W = 2.1 kW

User Joshua Underwood
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