hey..

do you remember stefan's law...

that E = AT⁴

 

newton took that difference b/n the surroundings and body be smalll

let that differnce be T

and temp. of surrounding be T₀

 

then, heat radated from the body will be

dQ/dt =  A{( T₀ + T)⁴  - T_{0  raised to the power} 4}     

         = AT_0^⁴ {(1 + T/T₀ )⁴ -1 }

let AT₀ ^4 = k as it is a constant

so...

mC(dT/dt) = k* ( 1 + (4T/T₀ ) - 1)  after binomial expansion.....

as del T is very small compared to T

-1 and +1 will get cancelled in the brackets...

rearranging ...

we will get dT/dt is directly proportional to del T......

as all other units are constant.... so dT/dt = K T  where K is constant....

it is the exact stament of newtons law of cooling......

if you integrate the above equation....

 you will get you will get temp. T after time 't' will be equal to

T_t  = T₀  + { T_initial  - T₀} e^-Kt