A body cools in a surrounding of constant temperature `30^@C` Its heat capacity is `2 J//^(@)C`. Initial temeprature of cooling is `40^@C` and assuming newtons law of cooling is valid. The body cools to `38^@C` in 10 min
In further 10 min it will cools from `38^@C` to _____

Options

A. `36^(@)C`
B. `36.4^(@)C`
C. `37^(@)C`
D. `37.5^(@)C`

Explanation

We have `theta-theta_(S)=(theta_(0)-theta_(S))e^(-k1)`
where `theta_(0)=` initial temperature of body `=40^(@)C`
`theta=` temperature of body after time `t`.
Since body cools from 40 to 38 in 10 min we have
`38-30=(40-30)e^(-k10)` ..(1)
Let after 10 min, the body temp be `theta`
`theta-30=(38-30)e^(-k10)` ...(2)
`((1)/(2))` gives `(8)/(theta-30)=(10)/(8).theta-30=6.4impliestheta=36.4.^(@)C`