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 C1:3 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 AmA=43π(DA2)3×ρA
and
Mass of sphere BmB=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