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Newton's Law of Cooling | Physics Class 11 - NEET PDF Download

8. Newton's law of cooling

According to this law, if the temperature T of the body is not very different from that of the surroundings T0, then rate of cooling - Newton`s Law of Cooling | Physics Class 11 - NEET is proportional to the temperature difference between them. To prove it let us assume that

T = T0 + Dt

Newton`s Law of Cooling | Physics Class 11 - NEET

Newton`s Law of Cooling | Physics Class 11 - NEETNewton`s Law of Cooling | Physics Class 11 - NEET

if the temperature difference is small.

Thus, rate of cooling

Newton`s Law of Cooling | Physics Class 11 - NEET or Newton`s Law of Cooling | Physics Class 11 - NEET

as dT = dq or DT = Dq

8.1 Variation of temperature of a body according to Newton's law 

Suppose a body has a temperature qi at time t = 0. It is placed in an atmosphere whose temperature is q0. We are interested in finding the temperature of the body at time t, assuming Newton's law of cooling to hold good or by assuming that the temperature difference is small. As per this law,

Newton`s Law of Cooling | Physics Class 11 - NEETNewton`s Law of Cooling | Physics Class 11 - NEET

rate of cooling µ temperature difference

or Newton`s Law of Cooling | Physics Class 11 - NEET or Newton`s Law of Cooling | Physics Class 11 - NEET

Here Newton`s Law of Cooling | Physics Class 11 - NEET is a constant

Newton`s Law of Cooling | Physics Class 11 - NEET

Newton`s Law of Cooling | Physics Class 11 - NEET

From this expression we see that q = qi at t = 0 and q = qat t = ¥, i.e., temperature of the body varies exponentially with time from qi to q0 (< qi). The temperature versus time graph is a shown in figure.

Newton`s Law of Cooling | Physics Class 11 - NEET

Note : If the body cools by radiation from q1 to q2 in time t, then taking the approximation

Newton`s Law of Cooling | Physics Class 11 - NEET and Newton`s Law of Cooling | Physics Class 11 - NEET

The equation Newton`s Law of Cooling | Physics Class 11 - NEET    becomes

Newton`s Law of Cooling | Physics Class 11 - NEET

This form of the law helps in solving numerical problems related to Newton's law of cooling. 

8.2 Limitations of Newton's Law of Cooling : 

(a) The difference in temperature between the body and surroundings must be small

(b) The loss of heat from the body should be radiation only.

(c) The temperature of surroundings must remain constant during the cooling of the body.

Ex.20 A body at temperature 40°C is kept in a surrounding of constant temperature 20°C. It is observed that its temperature falls to 35°C in 10 minutes. Find how much more time will it take for the body to attain a temperature of 30°C. 

Sol.

Newton`s Law of Cooling | Physics Class 11 - NEET

for the interval in which temperature falls from 40 to 35°C

Newton`s Law of Cooling | Physics Class 11 - NEET

for the next interval
(30 - 20) = (35 - 20) e-kt Newton`s Law of Cooling | Physics Class 11 - NEET

Newton`s Law of Cooling | Physics Class 11 - NEET
Newton`s Law of Cooling | Physics Class 11 - NEET

Alter: (by approximate method)
for the interval in which temperature falls from 40 to 35°C

Newton`s Law of Cooling | Physics Class 11 - NEET
from equation  Newton`s Law of Cooling | Physics Class 11 - NEET
Newton`s Law of Cooling | Physics Class 11 - NEET
for the interval in which temperature falls from 35°C to 30°C

Newton`s Law of Cooling | Physics Class 11 - NEET

from equation (14.4)

Newton`s Law of Cooling | Physics Class 11 - NEET

⇒ required time,
Newton`s Law of Cooling | Physics Class 11 - NEET 

9. NATURE OF THERMAL RADIATIONS : (WIEN'S DISPLACEMENT LAW) 

From the energy distribution curve of black body radiation, the following conclusions can be drawn :

(a) The higher the temperature of a body, the higher is the area under the curve i.e. more amount of energy is emitted by the body at higher temperature.

(b) The energy emitted by the body at different temperatures is not uniform. For both long and short wavelengths, the energy emitted is very small.

Newton`s Law of Cooling | Physics Class 11 - NEET

(c) For a given temperature, there is a particular wavelength (lm) for which the energy emitted (El) is maximum

(d)  With an increase in the temperature of the black body, the maxima of the curves shift towards shorter wavelengths.

From the study of energy distribution of black body radiation discussed as above, it was established experimentally that the wavelength (lm) corresponding to maximum intensity of emission decreases inversely with increase in the temperature of the black body. i.e.

Newton`s Law of Cooling | Physics Class 11 - NEET

This is called Wien's displacement law.

Here b = 0.282 cm-K, is the Wien's constant.

The document Newton's Law of Cooling | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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FAQs on Newton's Law of Cooling - Physics Class 11 - NEET

1. What is Newton's Law of Cooling?
Ans. Newton's Law of Cooling is a mathematical equation that describes the cooling of an object when it is in contact with a surrounding medium at a different temperature. It states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of the surroundings.
2. How is Newton's Law of Cooling applied in real-life situations?
Ans. Newton's Law of Cooling is commonly used in various real-life situations, such as determining the cooling rate of hot beverages, analyzing the temperature changes in cooking processes, estimating the time it takes for food to cool down to a safe temperature for storage, and studying the heat transfer in meteorology and climate science.
3. What are the assumptions made in Newton's Law of Cooling?
Ans. Newton's Law of Cooling makes certain assumptions to simplify the mathematical model. These assumptions include a uniform temperature within the object, a uniform temperature within the surrounding medium, constant thermal conductivity, and no heat generation or absorption within the object.
4. How can Newton's Law of Cooling be expressed mathematically?
Ans. Mathematically, Newton's Law of Cooling can be expressed as: dT/dt = -k(T - Ts) Where dT/dt represents the rate of change of temperature with respect to time, k is the cooling constant, T is the temperature of the object, and Ts is the temperature of the surroundings.
5. Can Newton's Law of Cooling be used for objects that are undergoing phase changes?
Ans. No, Newton's Law of Cooling is not applicable to objects undergoing phase changes, such as boiling or condensation. During phase changes, the temperature remains constant despite the addition or removal of heat. Different equations, like the latent heat equation, need to be used to analyze the cooling or heating of objects undergoing phase changes.
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