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# Newton'S Law of Cooling is a Special Case of - Physics

ConceptNewton’s Law of Cooling

#### Question

Newton's law of cooling is a special case of

• Wien's displacement law

• Kirchhoff's law

• Stefan's law

• Planck's law

#### Solution

Stefan's law

From Stefan-Boltzman's law, the energy of the thermal radiation emitted per unit time by a blackbody of surface area A is given by, u = σAT^4
Where σ  is Stefan's constant.
Suppose a body at temperature T is kept in a room at temperature T0.

According to Stefan's law, energy of the thermal radiation emitted by the body per unit time is u = eσAT^4
Here, e is the emissivity of the body.
The energy absorbed per unit time by the body is (due to the radiation emitted by the walls of the room
Δu = eσAT_0^4
Thus, the net loss of thermal energy per unit time is
Δu = eσA ( T^4 - T_0^4 )
Newton law of cooling is given by
(dT)/(dt) = -bA( T - T_0 )
This can be obtained from equation (i) by considering the temperature difference to be small and doing the binomial expansion.

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#### APPEARS IN

HC Verma Solution for Concepts of Physics - Vol. 2 (2018 to Current)
Chapter 6: Heat Transfer
MCQ | Q: 7 | Page no. 97
Solution Newton'S Law of Cooling is a Special Case of Concept: Newton’s Law of Cooling.
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