Physics cooler You have decided to make a large cooler to store meat. In order t
ID: 1400408 • Letter: P
Question
Physics cooler
You have decided to make a large cooler to store meat. In order to estimate the cost of the cooling unit
required you decide to model your cooler as a styrofoam rectangular prism with the following interior
dimensions: 3.0 m length, 2.5 m width, 2.0 m height. Wall thickness is 15 cm.
1. Calculate the net rate of heat
ow per second out of the cooler if the interior temperature is 5 C and
the exterior temperature can be 45 C.
2. Suppose you purchase a heat pump with a COP of 2.8. Calculate the pump power rating required to
maintain the internal temperature of the cooler.
Explanation / Answer
1. Net heat trasnfer rate Q = K A (T ext - T int)/ X
Where A is area of cross section of heat transfer = width x thickness
length L = 3 m, width B = 2.5 m: height H = 2 m: thi ckness X = 0.15 m
so , A = 2.5 x 0.15 = 0.375 sq mtr
K = thermal conductivity of styrofoam = 0.33 W/m K
So Q = 0.33 x .375 x (45-5)/0.15 = 33 J/s =33 Watt
Hence, Rate of heat = Q = 33 Watts.
2. COP of heat pump = desired effect/ heat transferred = Power rating/ Q
COP = Power rating required for heat pump/ Q
Power rating required = 2.8*33 =92.4 Watts
Hence, Power = 92.4 watts.