A body cools from `50.0^(@)C` to `49.9^(@)C` in 10s. How long will it take to cool from `40.0^(@)C` to `39.9^(@)C` ? Assume the temperature of the surrounding to be `30.0^(@)C` and Newton's law of cooling to be valid.

Options

A. 10 s
B. 20 s
C. 2.5 s
D. 5 s

Answer

B

Explanation

As per Newton's law of cooling, in the first case
`((50-49.9)/10)prop(49.95-30)i.e.prop19.95`
and in the second case,
`((40-39.9)/10)prop(39.95-30)prop9.95`
i.e. the temperature difference becomes half
`therefore` The rate of cooling will be half and hence it will take 20 s to cool from `40^(@)C to 39.9^(@)C`.