A body cools from 3T to 2T in 10 minutes. The room temprature is T. Assume that Newton's law of cooling is applicable. The temprature of body at end of next 10 minutes will be (A) 7/4 T (B) 3/2 T (C) 4/3 T (D) T?

Question

Answer

Answer

Answer

Introduction:
In this problem, we are given that a body cools from 3T to 2T in 10 minutes, where T represents the room temperature. We need to determine the temperature of the body at the end of the next 10 minutes. We will use Newton's law of cooling to solve this problem.

Newton's Law of Cooling:
Newton's law of cooling states that the rate of change of the temperature of an object is directly proportional to the difference between its temperature and the surrounding temperature.

Application of Newton's Law of Cooling:
Let's assume the temperature of the body at any given time t is represented by T(t). According to Newton's law of cooling, we can write the following differential equation:

(dT/dt) = -k(T - T0)

Where:
- dT/dt represents the rate of change of temperature with respect to time.
- k is a constant of proportionality.
- T is the temperature of the body at time t.
- T0 is the temperature of the surrounding (room temperature).

Solving the Differential Equation:
We can solve the differential equation to find the temperature function T(t). Integrating both sides of the equation, we get:

∫(1/(T - T0)) dT = -∫k dt

This gives us:

ln|T - T0| = -kt + C

Where C is the constant of integration.

Initial Conditions:
We are given that the body cools from 3T to 2T in 10 minutes. Therefore, we can use these initial conditions to determine the constant of integration C.

When t = 0, T = 3T
When t = 10, T = 2T

Substituting these values into the equation, we get:

ln|3T - T0| = C
ln|2T - T0| = -10k + C

Taking the difference of the above two equations, we get:

ln|3T - T0| - ln|2T - T0| = 10k

Simplifying this equation, we get:

ln((3T - T0)/(2T - T0)) = 10k

Temperature at the End of the Next 10 Minutes:
Now, we need to find the temperature of the body at the end of the next 10 minutes, which means when t = 20.

Using the equation ln|T - T0| = -kt + C, we can substitute t = 20 and solve for T:

ln|T - T0| = -20k + C

Since C is a constant, we can rewrite it as:

ln|T - T0| = ln((3T - T0)/(2T - T0))

From this equation, we can eliminate the natural logarithm by taking the exponential of both sides:

|T - T0| = (3T - T0)/(2T - T0)

Simplifying this equation, we get:

2T - T0 = 3T - T0

T = 2T

Therefore, the temperature of the body at the end of the next 10 minutes will be T.

Conclusion:
According to the given conditions and the application of Newton's law of cooling, we have

Similar NEET Doubts

A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from room temperature 20oC ? The temperature of boiling water is 100oC

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from room temperature 20ºC? The temperature of boiling water is 100ºC.

A body takes 5 minutes for cooling from 50°C to 40°C. Its temperature comes down to 33.33°C in next 5 minutes. Temperature of surroundings is

Bacterial cell divides every one minute. It takes 15 minutes a cup to be filled one-fourth. How much time will it take to fill the cup full? (

Top Courses for NEETView all

Biology Class 11

Daily Test for NEET Preparation

NEET Mock Test Series 2025

Topic-wise MCQ Tests for NEET

Physics Class 11

Top Courses for NEET

Top Courses for NEET

Suggested Free Tests

Related Content

About NEET

NEET Preparation Material

How to Prepare for NEET Exam?

NCERT Based Study Material

NEET Mock Tests

Other Popular Exams

Company