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  • Perplex
    IB Math AIHL
    /
    Modelling
    /

    Problem Bank

    [Maximum mark: 14]

    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

    ​
    Q∝wT2A​
    ​

    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.

    1. Find the value of ​k.

      [3]

      To earn a crown, get your answer ready before you reveal the options!

    The temperature inside cube ​Y​ is increased by ​n°C​ such that the two cubes lose heat at the same rate.

    1. Find the value of ​n.

      [3]

    A third cube ​Z​ with internal temperature ​10°C​ loses heat at the same rate as ​X.

    1. Given that the internal volume of ​Z​ is ​1m3, find the thickness of its walls.

      [8]

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