Question

According to Newton's law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta)^{n}$ where $\Delta \theta$ is the difference between the temperature of the body and the surrounding. Then $n$ is equal to (A) 2 (B) 3 (C) 4 (D) 1

Name: Problem 36, Chapter 11: A Complete Resource Book in Physics for JEE Main
Uploaded: 2022-02-11T07:08:37-08:00
Duration: 1 min 51 s
Channel: Rubeena Zulfiqar
Description: According to Newton's law of cooling, the rate of cooling of a body is proportional to (Δθ)^n where Δθis the difference between the temperature of the body and the surrounding. Then n is equal to (A) 2 (B) 3 (C) 4 (D) 1

   According to Newton's law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta)^{n}$ where $\Delta \theta$ is the difference between the temperature of the body and the surrounding. Then $n$ is equal to
(A) 2
(B) 3
(C) 4
(D) 1

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 11, Problem 36

Instant Answer

Solved by Expert Rubeena Zulfiqar

02/11/2022

Step 1

Mathematically, this can be represented as: \[ \frac{d\theta}{dt} \propto \Delta \theta \] where $\frac{d\theta}{dt}$ is the rate of cooling and $\Delta \theta$ is the temperature difference between the body and the surroundings. Show more…

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According to Newton's law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta)^{n}$ where $\Delta \theta$ is the difference between the temperature of the body and the surrounding. Then $n$ is equal to (A) 2 (B) 3 (C) 4 (D) 1

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Key Concepts

Newton's Law of Cooling

Newton's Law of Cooling states that the rate at which an object cools (or heats) is proportional to the difference between its temperature and that of its surroundings. This principle is frequently modeled using a first-order differential equation, which results in an exponential decrease (or increase) in temperature over time under constant ambient conditions.

Direct Proportionality

Direct proportionality refers to a relationship where one quantity is directly related to another by a constant multiplier. In the context of Newton's Law of Cooling, the rate of temperature change is directly proportional to the temperature difference raised to the first power, indicating a linear relationship between the cooling rate and the temperature difference.

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