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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a
tanϕ2tanϕ1=θ1−θ0θ2−θ0
b
tanϕ2tanϕ1=θ2−θ0θ1−θ0
c
tanϕ1tanϕ2=θ1θ2
d
tanϕ1tanϕ2=θ2θ1
answer is B.
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Detailed Solution
For θ−t plot, rate of cooling =dθdt= slope of the curve. At P,dθdt=tanϕ2=k(θ2−θ0), where k= constant. At Q, dθdt=tanϕ1=kθ1−θ0⇒tanϕ2tanϕ1=θ2−θ0θ1−θ0
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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