First slide

Heat capacity

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

Moderate

A

1 : 6
B

1 : 12
C

1 : 3
D

1 : 4

Solution

$\begin{array}{l} \frac{m_{A} C_{A}}{m_{B} C_{B}} = \frac{(4 / 3) {πr}_{A}^{3} ρ_{A} C_{A}}{(4 / 3) {πr}_{B}^{3} ρ_{B} C_{B}} \\ = {(\frac{r_{A}}{r_{B}})}^{3} \frac{ρ_{A} C_{A}}{ρ_{B} C_{B}} \\ = {(\frac{1}{2})}^{3} (\frac{2}{1}) (\frac{1}{3}) = \frac{1}{12} . \end{array}$

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