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Two sphere of radii in the ratio 1 : 2, ...

Two sphere of radii in the ratio `1 : 2`, have specific heats in the ration `2 : 3`. The densities are in the ratio `3 : 4`. Find the ration of their thermal capacities.

Text Solution

Verified by Experts

Thermal capacity of a body `= mS`
The ratio of thermal capacities
`(m_(1)S_(1))/(m_(2)S_(2)) = (V_(1)rho_(1)S_(1))/(V_(2)rho_(2)S_(2)) = ((4)/(3)pi r_(1)^(3) rho_(1)S_(1))/((4)/(3) pi r_(2)^(3) rho_(2) S_(2)) = ((r_(1))/(r_(2)))^(3) ((rho_(1))/(rho_(2))) ((S_(1))/(S_(2)))`
Here, `(r_(1))/(r_(2)) = (1)/(2) ,(S_(1))/(S_(2)) = (2)/(3) , (rho_(1))/(rho_(2)) =(3)/(4)`
The ratio of thermal capacities
=`((1)/(2))^(3) ((3)/(4))((2)/(3)) =(1)/(16)`.
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