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

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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.

  Is there an error in this question or solution?

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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