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An insulated cube loses heat at a rate of Q joules per second. Heat loss Q through the walls of the cube can be modeled by
where
T°C is the temperature inside the cube,
Am2 is the external area, and
wm is the thickness of the insulated walls.
Cube X has a surface area of 4m2 and a wall thickness of 0.2m.
Cube Y has a surface area of 0.5m2 and a wall thickness of 0.1m.
The temperature inside both cubes is 20°C, and cube X loses heat k times as fast as cube Y.
Find the value of k.
The temperature inside cube Y is increased by n°C such that the two cubes lose heat at the same rate.
Find the value of n.
A third cube Z with internal temperature 10°C loses heat at the same rate as X.
Given that the internal volume of Z is 1m3, find the thickness of its walls.
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