Newton’s Law of cooling is an approximate form of

Concept: 

Newton's law of cooling:

• It a law that describes the rate at which an exposed body changes temperature through radiation.
• Heat Radiated is directly proportional to the difference between the object's temperature and its surrounding.
• The greater the difference in temperature between the system and surrounding more rapidly the heat is transferred. i.e. more rapidly the body temperature of body changes.
• Newtons law of cooling is given by,

• Tt = Temperature at time t 
• Ts = Temperature of the surrounding
• K = Positive constant that depends on the area and nature of the surface of the body under consideration.

Stefan’s law

• Stefan's Law: According to it the radiant energy emitted by a perfectly black body per unit area per sec (i.e. emissive power of black body) is directly proportional to the fourth power of its absolute temperature i.e.

E ∝ T ⁴ 

 -- (1)

Where, is a constant called Stefan’s constant.

• The value of Stefan's constant is 5.67 × 10-8 W/m2K4.

Explanation:

From Stefan's Law we can say that

 -- (2)

Δ T = T - T₀

⇒ T = T₀ + Δ T ---- (3)

Putting (3) in (2)

⇒ 

⇒ 

(1 + x)n = 1 + nx (by binomial theorm for very small value of x. 

e. σ, T₀ are constant.

or

This is basically Newtons Law of cooling.