# Which of the following is special form of Newton's law of cooling?

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Which of the following is special form of Newton's law of cooling?
1. Wien's Law of Displacement
2. Kirchhoff's Law
3. Planck's Law
4. Stephen's Law

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Correct Answer - Option 4 : Stephen's Law

Concept:

• Stephen's Boltzmann's law: According to Stefan Boltzmann law, The amount of radiation emitted per second per unit area by a black body is directly proportional to the fourth power of its absolute temperature.

E ∝ T4
E = σ T4

This law is true for only ideal black body

where T = temperature of an ideal black body (in K)

Stephen's constant σ = 5.67 x10–8 watt /m2 K4

SI Unit : E = watt/m2

• Newton's law of cooling: Rate of loss of heat is directly proportional to excess of temperature of the body over that of surrounding.

$\frac{dQ}{dt} \propto T - T_∘$

Where,

T = temperature of body.

T  = temperature of surrounding

• Wien's Law of Displacement: It states that black body radiation has different peaks of temperature at wavelengths that are inversely proportional to temperatures.
• Kirchhoff's Law: At a given temperature for all bodies the ratio of their spectral emissive power to spectral absorptive power is constant and this constant is equal to spectral emissive power of the ideal black body at same temperature.
• Plank law: The electromagnetic radiation from heated bodies is not emitted as a continuous flow but is made up of discrete units or quanta of energy.

Explanation:

From the above discussion, we can say that,

• Newton's law of cooling can be derived from Stephen Boltzmann law.
• When the temperature difference is very small, Stefan's law can be converted to Newton's law of cooling.
• Newton's law of cooling doesn't take the fact that a body can cool by both radiation and convection, it takes only radiation.

​Hence, Stephen law is the special form of Newton's law of cooling.