A body cools from `60^@`C to `50^@`C in 10 min. Find its temperature at the end of next 10 min if the room temperature is `25^@C`. Assume Newton's law of cooling holds.

Options

A. `45^(@)C`
B. `42.85^(@)C`
C. `40^(@)C`
D. `38.5^(@)C`

Answer

B

Explanation

According to Newton's law of cooling.
`(theta_(1)-theta_(2))/(t)prop((theta_(1)+theta_(2))/(2)-theta_(0))`
`:.(60-50)/(20)prop((60+50)/(2)-25)" "...(i)`
`(50-theta)/(20)prop((50+theta)/(2)-25)" "...(ii)`
`:.(60-50)/(20)xx(20)/(50-theta)=(((110)/(2)-25))/(((50+theta)/(2)-25))`
`implies(10)/(50-theta)=(60)/(theta)`
`implies" "10theta=3000-60theta`
`:." "theta=42.85^(@)C`