Question

two sphers A and B have diameters in ratio 1:2 densities in ratio 2:1 and specific heat in ratio1:3 finf ratio of thermal capacity

Answer 1

Answer on Question #73035, Physics / Molecular Physics | Thermodynamics

Two spheres A and B have diameters in ratio 1:2; densities in ratio 2:1; and specific heat in ratio 1:3. Find ratio of thermal capacity

Solution

$$C = cm = c\rho V = \frac{4\pi r^3c\rho}{3}$$

, where C – thermal capacity, c – specific capacity, $\rho$ – density, V – volume.

Remove the constants:

C is proportional to $r^3 c\rho$.

$$\frac{D_A}{D_B} = \frac{1}{2} \Rightarrow \frac{r_A}{r_B} = \frac{1}{2} \Rightarrow \frac{r_A^3}{r_B^3} = \frac{1}{8};$$ $$\frac{c_A}{c_B} = \frac{1}{3};$$ $$\frac{\rho_A}{\rho_B} = \frac{2}{1};$$ $$\frac{C_A}{C_B} = \frac{r_A^3 c_A \rho_A}{r_B^3 c_B \rho_B} = \frac{1}{8} \times \frac{1}{3} \times \frac{2}{1} = \frac{1}{12}$$

Answer

The ratio of thermal capacities is 1:12.

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