Derive newton's law of cooling from stefan's law

Rate of cooling of the body is directly proportional  to the temperature difference of body and surrounding if temperature difference is small.

From Stefan's Law

Where A = Surface area of a body

T = Absolute temperature of body 

T₀ = Temperature of surrounding

If the temperature difference is small,

So, T = T₀ + ΔT

We neglect higher power of

Hence, 

The body may also lose energy due to convection in the surrounding air. It also depends on surface area and temperature difference of body.

Δu₂ = b₂ A (T – T₀)

The net rate of lose of thermal energy due to convection and radiation

Δu = Δu₁ + Δu₂ 

 = (b₁ + b₂) A (T – T₀)

Rate of fall of temperature is

Where m = mass of object

s = specific heat capacity

This is Newton’s law of cooling.