A bucket full of hot water cools from `75^(@)C` to `70^(@)C` in time `T_(1)`, from `70^(@)C` to `65^(@)C` in time `T_(2)` and from `65^(@)C` to `60^(@)C` in time `T_(3)`, then

Options

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

Answer

A

Explanation

By Newton's law of cooling
`(dH)/(dt)=K((theta_(1)+theta_(2))/(2)-theta_(0))`
where, `theta_(0)` is the temperature of surrounding and `(theta_(1)+theta_(2))/(2)` is the temperature of body.
Hence, `t_(3) gt t_(2) gt t_(1)`