Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown, with their ends at 1000C, 500C and 00C. The temperature of their junction is

A
$75^{0} C$
B
${\frac{100}{3}}^{0} C$
C
${\frac{200}{3}}^{0} C$
D
$40^{0} C$

Solution:

$\begin{array}{l} Let T be the temperature of the junction. \\ {The thermal currents I= I}_{1} + I_{2} \\ \frac{100 - T}{l / 3 KA} = \frac{T - 50}{l / 2 KA} + \frac{T - 0}{l / KA} \\ 3 (100 - T) = 2 (T - 50) + T \\ \Rightarrow T = {(\frac{200}{3})}^{0} C \end{array}$

Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown, with their ends at $100^{0} C, 50^{0} C a n d 0^{0} C . The temperature of their junction is$

Solution:

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