IIT JEE , AIEEE Forum - Physics , Thermal Physics

eistien

hey everybody plz check in arihant waves and thermodynamics pg no 167 and could you explain to me about that approximation he has done in calculating the variation of temperature of a body by newton's law of cooling???rates assured!!!

coolvignesh

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 + (4

T/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

saurabh_me

ya sure friend,.

well u can check out the real proof from any book.....i m jst telling the assumptions made in proof,....

1. the temperature of surroundings is considered as constant.

2. due to this the value of temp. of body minus temp. of surrounding can be taken as temp. of surrounding.

and hence ultimately we get the equation dT/dt

Temp. of body minus temp. of surroundings....

well this law is full of assumptions and it cant be used generally....

thanks for sharing the doubt....

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