First slide

Heat capacity

Question

Two spheres of radii in the two ratios 2 : 3 have specific heat in the ratio 3 : 2. What is the ratio of their thermal capacities?

Moderate

A

3 : 2
B

4 : 1
C

2 : 9
D

4 : 9

Solution

Thermal capacity is
$m \cdot s = (\frac{4}{3} {πR}^{3}) \cdot sd$
where d is the density of the body.
$= \frac{Thermal capacity of first sphere}{Thermal capacity of second sphere} = \frac{(4 {πR}_{1}^{3} / 3) s_{1} d}{(4 {πR}_{2}^{3} / 3) s_{2} d}$
$\begin{array}{l} = {(\frac{R_{1}}{R_{2}})}^{3} (\frac{s_{1}}{s_{2}}) \\ = {(\frac{2}{3})}^{3} (\frac{3}{2}) = 4 : 9 \end{array}$

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