A bucket full of hot water is kept in a room. It cools from `75^(@)C` to `70^(@)C` in `t_(1) `minutes, from `70^(@)C` to `65^(@)C` in `t_(2)` minutes and from `65^(@)C` to `60^(@)C` in `t_(3)` minutes. Then

Options

A. `t_(1) lt t_(2) lt t_(3)`
B. `t_(1)=t_(2)=t_(3)`
C. `t_(1) lt t_(2) gt t_(3)`
D. `t_(1) gt t_(2) gt t_(3)`

Answer

A

Explanation

According to Newton.s law of cooling is proportional to the mean excess of temperature of the body over the surroundings. If temperature of surroundings be `theta`, then
`R_(1)prop(72.5-theta)tot_(1)`
`R_(2)prop(67.5-theta)tot_(2)`.
`R_(3)prop(62.5-theta)tot_(3)`.
This gives `t_(1) lt t_(2) lt t_(3)`.