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Question

Two spheres A and B have diameters in the ratio 1:2, densities in the ratio 2:1 and thermal capacities in the ratio 1:12. Find the ratio of their specific heat capacities.

A
1:6
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B
1:12
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C
1:3
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D
1:4
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Solution

The correct option is C 1:3
We know that
Mass = Volume × Density (ρ)
and
Volume of sphere V=43π(D2)3
Where D is the diameter of sphere.
Mass of sphere A mA=43π(DA2)3×ρA
and
Mass of sphere B mB=43π(DB2)3×ρB
mAmB=43π(DA2)3ρA43π(DB2)3ρB=D3AρAD3BρB
Also,
We know
Thermal capacity (C)=ms
where (s) is specific heat capacity.
CACB=mAsAmBsB=112
sAsB=112×mBmA
sAsB=112×D3BρBD3AρA
sAsB=112×(21)3×12
sAsB=13

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