A company wants to market a picnic cooler guaranteed to keep drinks below for at…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A company wants to market a picnic cooler guaranteed to keep drinks below 10∘C for at least 4 hours in direct summer sunlight. The cooler consists of a plastic shell lined with a uniform layer of insulating foam. The design team is comparing two commercially available foams with the properties shown below.
Foam Type
Thermal Conductivity k (W m−1 K−1)
Density (kg m−3)
Cost (USD m−3)
Foam A
0.030
45
85
Foam B
0.018
60
160
Both cooler models have an interior surface area of 0.50m2 and initial internal temperature of 4∘C. During field testing the exterior surface is held at 35∘C by solar heating.
(a) Without performing explicit calculations, compare the qualitative effectiveness of Foam A and Foam B as insulators. Base your reasoning solely on the values in the table.
(b) The design team specifies a wall thickness of L=25mm. Assuming steady-state conditions and one-dimensional conduction, calculate the thermal energy transferred into the cooler over the 4-hour period for each foam type. Provide your answers in kilojoules.
(c) After considering results from part (b) as well as the listed material cost, recommend which foam the company should select. Defend your recommendation by discussing both thermal performance and economic factors.