Ratio between the densities and specific heats of the materials of two bodies are `2:3` and `0.12 : 0.09` respectively . If their volumes are in the ratio `7:8,` what is the ratio of thermal capacities?

Explanation

Let the density of the first substance be `d_(1)`, its specific heat `s_(1)` and volume `V_(1)`.
Also, let the density, specific heat and volume for the second body be `d_(2),s_(2) and V_(2)` respectively.
Hence, thermal capacity of the first one,
`C_(1)=m_(1)s_(2)=V_(1)d_(1)s_(1)`
and that of the second body, `C_(2)=m_(2)s_(2)=V_(2)d_(2)s_(2)`
`therefore" "(C_(1))/(C_(2))=(V_(1))/(V_(2))xx(d_(1))/(d_(2))xx(s_(1))/(s_(2))=(7)/(8)xx(2)/(3)xx(0.12)/(0.09)=(7)/(9)`
Hence, their thermal capacities are in the ratio of `7:9`.