Certain quantity of water cools from `70^(@)C` to `60^(@)C` in the first 5 minutes and to `54^(@)C` in the next 5 minutes and to `54^(@)C` in the next 5 minutes. The temperature of the surroundings is

Options

A. `45^(@)C`
B. `20^(@)C`
C. `42^(@)C`
D. `10^(@)c`

Answer

A

Explanation

For the first 5 minutes,
`(T_(2)-T_(1))/(t)=-k[(T_(1)+T_(2))/(2)-T]`
`:.(60-70)/(5)=-k[(60+70)/(2)-T]`
`:.-2=-k[65-T` . . . (1)
For the next 5 minutes,
`(54-60)/(5)=-k((54+60)/(2)-T)`
`:.-(6)/(5)=-k(57-T)` . . . (2)
Dividing equation (1) by equation (2),
`(10)/(6)=(65-T)/(57-T)`
`:.570-10T=390-6T`
`:.570-390=10T-6T`
`:.180=4T`
`:.T=(180)/(4)`
`:.T=45^(@)C`