If the ratio of radii of two spheres of same material is 1:4, then the ratio of their heat capacities will be:
A
1/64
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B
1/32
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C
1/2
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D
1/4
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Solution
The correct option is A1/64 As material of both the spheres is same, therefore their specific heat capacity (s) and density will also be same.
Also, Mass(m)=Volume(V)×density(ρ)
For sphere;
Volume (V)=43×π×r3 ∴ Mass of 1st sphere; mA=VA×ρA =43πr3A×ρA
and
Mass of 2nd sphere, mB=43πr3B×ρB Heat capacity(C)=Mass(m)×Specific heat capacity (s) ∴CACB=mAsAmBsB=r3AρAr3BρB=r3Ar3B∵ρA=ρB∴CACB=(14)3⇒CACB=164