The amount of heat flows in time
t through a cylindrical metallic rod of length
L and uniform area of cross section
A(=Ï€R2) with its ends maintained at temperatures
T1 and
T2(T1>T2) is given by
Q=‌t .....(i)
where
K is the thermal conductivity of the material of the rod.
Area of cross-section of new
rod‌A′=π(‌)2=‌=‌.....(ii)
As the volume of the rod remains unchanged
∴‌‌AL=A′L′ where L' is the length the new rod
or
L′=L‌.......(iii)
=4L (Using (ii))
Now, the amount of heat flows in same time
t in the new rod with its ends maintained at the same temperatures
T1 and
T2 is given by
Q′=‌.....(iv)
Substituting the values of
A′ and
L′ from equations (ii) and (iii) in the above equation, we get
Q′=‌=‌‌ =‌Q‌‌( Using (i))