Question

Two spheres A and B have diameters in the ratio 1 : 2, densities in the ratio 2 : 1 and specific heats in the ratio 1 : 3; find

the ratio of their thermal capacities

Answer 1

The ratio of their thermal capacity will be 1:12

Explanation :

Let the radius of the 1st sphere = r

=> radius of the 2nd sphere = 2r

Let the density of the 1st sphere = 2ρ

=> density of the 2nd sphere = ρ

Let the specific heat of the 1st sphere = S

=> specific heat of the 2nd sphere = 3S

we know that

thermal capacity = mass x specific heat

=> C = m x S

=> C = Volume x density x specific heat

For sphere A

C₁ = V₁ x 2ρ x S

=> C₁ = 4/3 x πr³ x 2ρ x S

=> C₁ = 8/3 x πr³ρS

For sphere B

C₂ = V₂ x ρ x 3S

=> C₁ = 4/3 x π(2r)³ x ρ x 3S

=> C₁ = 32 πr³ρS

so the ratio of their thermal capacity

= C₁/C₂

=(8/3 x πr³ρS)/32 πr³ρS

=1/12

Hence the ratio of their thermal capacity will be 1:12