A pan filled with hot food cools form `94^(@)C` to `86^(@)C` in 2 minutes . When the roo temperature is `20^(@)C`. How long will it cool from `74^(@)C` to `66^(@)C` ?

Options

A. 2 minutes
B. 2.8 minutes
C. 2.5 minutes
D. 1.8 minutes

Answer

B

Explanation

From Newton.s law of cooling, `(d theta)/(dt)prop(theta-theta_(0))`
In Case (i), `(94-86)/(2)prop((94+86)/(2)-20)`
`implies (8)/(2)prop(90-20)`
or `4prop70" "….(1)`
In Case (ii), `(74-66)/(t)prop((74+66)/(2)-20)`
`(8)/(t)prop(70-20)`
`(8)/(t)prop50" "....(2)`
Dividing (1) and (2)
`(t)/(2)=(70)/(50)`
`t=(14)/(5)`
`t=2.8` minutes