Properties Of Solids And Liquids Question 455

Question: A body cools in a surrounding which is at a constant temperature of θ0 . Assume that it obeys Newton’s law of cooling. Its temperatureθ is plotted against time t. Tangents are drawn to the curve at the pointsP(θ=θ2) andQ(θ=θ1) . These tangents meet the time axis at angle ofϕ2 and ϕ1 , as shown, then

Options:

A) tanϕ2tanϕ1=θ1θ0θ2θ0

B) tanϕ2tanϕ1=θ2θ0θ1θ0

C) tanϕ1tanϕ2=θ1θ2

D) tanϕ1tanϕ2=θ2θ1

Show Answer

Answer:

Correct Answer: B

Solution:

[b] For 0-t plot, rate of cooling =dQdt= slope of the curve. ATP,dQdt=|tan(180ϕ2)|

=tanϕ2=k(θ2θ1) where k= constant. At Q, dQdt=|tan(180φ1)|=tanφ1,=k(θ1θ0)

tanϕ2tanϕ1=θ2θ0θ1θ0



NCERT Chapter Video Solution

Dual Pane