JEE Main 2013PhysicsThermal Properties of MatterEasyMCQ

JEE Main 2013 — Thermal Properties of Matter Question with Solution

JEE Main 2013 (07 Apr)

Question

If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ0, the graph between the temperature T of the metal and time t will be closest to :

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Show full solutionCorrect option: A
Correct answer
A

Step-by-step explanation

According to Newton's cooling law, rate of cooling is

dθdt∝θ-θ0

Here, θ=the temperature of the body

θ0=Room temperature(constant)

Let k be the proportionality constant and θi be the initial temperature.
Therefore, 

dθdt=-kθ-θ0⇒∫dθθ-θ0=-k∫dt⇒lnθ-θ0=-kt⇒θ=θ0+θ-θ0e-kt

Hence, the graph is exponential.

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About this question

This is a previous-year question from JEE Main 2013, covering the Thermal Properties of Matter chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.