A black body calorimeter filled with hot water cools from `60^(@)C` to `50^(@)C` in `4 min` and `40^(@)C` to `30^(@)C` in `8min`. The approximate temperature of surrounding is :

Options

A. `10^(@)C`
B. `15^(@)C`
C. `20^(@)C`
D. `25^(@)C`

Explanation

`(d theta)/(dt)=k(Deltatheta)=k[theta_(w)-theta_(s)]`
`theta_(s)=` Temperature of surrounding
`theta_(w)=(theta_(1)+theta_(2))/(2)`
`(10)/(4)=k[(60+50)/(2)-theta_(s)]`……..`(i)`
`(10)/(8)=k[(40+30)/(2)-theta_(s)]`……..`(ii)`
equation `(i)` divided by `(ii)` gives
`z=(55-theta)/(35-theta)`
`70-20theta=55-theta`
`theta=15^(@)`