NEET-XII-Physics
28: Heat Transfer
- #7Newton’s law of cooling is a special case of
(a) Wien’s displacement law
(b) Kirchhoff’s law
(c) Stefan’s law
(d) Planck’s lawdigAnsr: cAns : (c) 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=\sigma A{T}^{4}``
Where `` \sigma `` 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=e\sigma A{T}^{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)
`` {u}_{0}=e\sigma A{{T}_{0}}^{4}``
Thus, the net loss of thermal energy per unit time is
`` ∆u=u-{u}_{0}``
`` ∆u=e\sigma A({T}^{4}-{{T}_{0}}^{4})...\left(\,\mathrm{\,i\,}\right)``
Newton law of cooling is given by
`` \frac{\mathit{d}T}{\mathit{d}t}=-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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