Variable thermal conductivity!

Classical Mechanics Level 4

A rod of length l l with thermally insulated lateral surface is made of a material whose thermal conductivity varies as K = C T K =\dfrac C T , where C C is a constant. The ends are kept at temperatures T 1 T_1 and T 2 T_2 . The temperature at a distance x x from the first end varies as T = T 1 ( T 2 T 1 ) a x 2 l T= T_1 \large(\frac{T_2}{T_1})^{\frac{ax}{2l}} . Find the value of ' a a '.


The answer is 2.

Nishant Rai by Nishant Rai , 25, India

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2 solutions

Nishant Rai
May 30, 2015

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Rohit Ner
May 30, 2015

At the other end where the temperature is T 2 {T}_{2} , x = l x=l ,

T 2 = T 1 ( T 2 T 1 ) a x 2 l {T}_{2}=T_1 \large(\frac{T_2}{T_1})^{\frac{ax}{2l}}

T 2 T 1 = ( T 2 T 1 ) a l 2 l \large\frac{T_2}{T_1}=\large(\frac{T_2}{T_1})^{\frac{al}{2l}}

a = 2 a=\boxed 2

2 Helpful 0 Interesting 0 Brilliant 0 Confused

same way!!!!!

A Former Brilliant Member - 3 years, 7 months ago

Savage!!! Haha

Md Zuhair - 3 years, 5 months ago

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