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Thermal Expansion of Spheres

  1. Oct 24, 2011 #1
    Explain why the thermal expansion of a spherical shell made of a homogeneous solid is equivalent to that of solid sphere of the same material.



    I guess these equations would be of some help.
    (ΔA)=A*2α*(ΔT)
    α→ Coefficient of linear expansion.
    A→ Area
    T→ Temperature

    (ΔV)=V*3α*(ΔT)
    α→ Coefficient of linear expansion.
    V→ Volume
    T→ Temperature




    I'm not sure if i understood the question right.
    By "equivalent thermal expansion" i guess they mean to say the radius increases by same amount during the expansion.
    So i set out relating the two radii.
    Took two spheres, one hollow, the other solid, of same dimensions, i.e., same radii.



    For the Shell,

    (ΔA)=A*2α*(ΔT)
    Rf2-Ri2=Ri2*2α*ΔT
    Rf=Ri√(2α*ΔT+1)

    For the solid sphere, similarly, relating the volume,
    Rf=Ri∛(3α*ΔT+1)


    But, failed to prove them to be the same.
    So what exactly do they intend to ask? And how do i hit it?...
     
  2. jcsd
  3. Oct 25, 2011 #2
    Does this work?
     

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