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A body cools in a surrounding which is a...

A body cools in a surrounding which is at constant temperature of `theta_(0)`. Assume that it obeys Newyon's law of colling. Its temperature `theta` is plotted against time `t`. Tangents are drawn to the curve at the points `P(theta=theta_(t))` and `Q(theta=theta_(2))`. These tangents meet the time axis at angles of `phi_(2)` and `phi_(1)`, as shown

A

`(tanphi_(2))/(tanphi_(1))=(theta_(1)-theta_(0))/(theta_(2)-theta_(0))`

B

`(tanphi_(2))/(tanphi_(1))=(theta_(2)-theta_(0))/(theta_(1)-theta_(0))`

C

`(tanphi_(1))/(tanphi_(2))=(theta_(1))/(theta_(2))`

D

`(tanphi_(1))/(tanphi_(2))=(theta_(2))/(theta_(1))`

Text Solution

Verified by Experts

The correct Answer is:
B
For `theta-t` plot, rate of cooling `=(dtheta)/(dt)=` slope of the curve
At `P`, `(dtheta)/(dt)=tanphi_(2)=k(theta_(2)-theta_(0))`, where `k` is constant.
At `Q`, `(dtheta)/(dt)=tanphi_(1)=k(theta_(1)-theta_(0))`
`:. (tanphi_(2))/(tanphi_(1))=(theta_(2)-theta_(0))/(theta_(1)-theta_(0))`
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