The initial temperature of a body is `80^(@)C`. If its temperature falls to `64^(@)C` in `5` minute and in `10` minute to `52^(@)`. Find the temperature of surrounding.

Options

A. `26^(@)C`
B. `60^(@)C`
C. `36^(@)C`
D. `49^(@)C`

Answer

D

Explanation

According Newton's law, `(theta_(1)-theta_(2))/(t) = k[(theta_(1)+theta_(2))/(2)- theta_(0)]`
Initially, `((80-64))/(5) = K((80+64)/(2)- theta_(0))`
`+rArr 3.2 -K[72-theta_(0)]` ...(i)
Finally, `((64-52))/(10) = K[(64+52)/(2)-theta_(0)]`
`rArr 1.2 = K[58-theta_(0)]` ...(ii)
On solving equation (i) and (ii) `theta_(0) = 49^(@)C s`.