First slide

Calorimetry

Question

Two sphere’s of radii in the ratio 1:2, have specific heats in the ratio 2:3. If their densities are in the ratio 3:4, find the ratio of their thermal capacities.

Moderate

A

16:1
B

1:16
C

4:3
D

3:4

Solution

$r a t i o o f r a d i i i s \frac{r_{1}}{r_{2}} = \frac{1}{2} ratio of specific capacities is \frac{S_{1}}{S_{2}} = \frac{2}{3} r a t i o o f d e n s i t i e s i s \frac{ρ_{1}}{ρ_{2}} = \frac{3}{4} t h e r m a l c a p a c i t y = m a s s x s p e c i f i c h e a t = d e n s i t y x v o l u m e x s p e c i f i c h e a t r a t i o o f t h e r m a l c a p a c i t i e s i s \frac{m_{1} S_{1}}{m_{2} S_{2}} = \frac{ρ_{1}}{ρ_{2}} \times {(\frac{{πr}_{1}}{{πr}_{2}})}^{3} \times \frac{S_{1}}{S_{2}} \frac{m_{1} S_{1}}{m_{2} S_{2}} = \frac{3}{4} \times \frac{1}{8} \times \frac{2}{3} = \frac{1}{16} m_{1} S_{1} {:m}_{2} S_{2} = 1 : 16 = r a t i o o f t h e r m a l c a p a c i t i e s$

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