A body cools in a surrounding which is at a constant temperature of θ$$0$$. Assume that it obeys Newton's law of cooling. Its temperature θ is plotted against time t. Tangents are drawn to the curve at the points Pθ$$=$$θ$$2$$ and Qθ$$=$$θ$$1$$. These tangents meet the time axis at angles of ϕ$$2$$ and ϕ$$1$$, as

Question

A body cools in a surrounding which is at a constant temperature of θ$$0$$. Assume that it obeys Newton's law of cooling. Its temperature θ is plotted against time t. Tangents are drawn to the curve at the points Pθ$$=$$θ$$2$$ and Qθ$$=$$θ$$1$$. These tangents meet the time axis at angles of ϕ$$2$$ and ϕ$$1$$, as

Infinity Learn · Accepted Answer

For θ−t plot, rate of cooling $$=d$$θ$$dt=$$ slope of the curve.  At  P,dθ$$dt=$$$$tan$$⁡ϕ$$2=k($$θ$$2$$−θ$$0)$$, where $$k=$$ constant.  At  Q, dθ$$dt=$$$$tan$$⁡ϕ$$1=k$$θ$$1$$−θ$$0$$⇒$$tan$$⁡ϕ$$2tan$$⁡ϕ$$1=$$θ$$2$$−θ$$0$$θ$$1$$−θ$$0$$

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A body cools in a surrounding which is at a constant temperature of θ0. Assume that it obeys Newton's law of cooling. Its temperature θ is plotted against time t. Tangents are drawn to the curve at the points Pθ=θ2 and Qθ=θ1. These tangents meet the time axis at angles of ϕ2 and ϕ1, as

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