A body cools in 7 min from `60^@C` to `40^@C`. What will be its temperature after the next 7 min? The temperature of surroundings is `10^@C`.

Options

A. `28^@C`
B. `25^@C`
C. `30^@C`
D. `22^@C`

Answer

A

Explanation

According to Newton's law of cooling
`[(theta_1-theta_2)/(t)]=K[((theta_1+theta_2)/(2))-theta_0]`
So that `[(60-40)/(7)]=K[((60+40)/(2))-10]`
`impliesK=(1)/(14)`
Now if after cooling from `40^@C` to 7 min the temperature of the body becomes `theta`, according to Newton's law of cooling,
`[(40-theta)/(7)]=K[((40+theta)/(2))-10]`
Which in the light of Eq. (i) i.e., `K=(1//14)`, gives
`[(40-theta)/(7)]=(1)/(14)[((20+theta)/(2))]`
`160-4theta=20+theta`,`theta=28^@C`