Question

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

• A. ${75}^{o}C$
• B. ${\frac{200}{3}}^{o}C$
• C. ${40}^{o}C$
• D. ${\frac{100}{3}}^{o}C$

Answer 1

Answer: (B)

${\frac{200}{3}}^{o}C$

Let the temperature at the point of contact of three rod is $T$,as we know that total incoming of heat is equal to total outgoing heat.
we know that heat flow is given as

$Q=\frac{KA\left(\Delta T\right)}{L}$

so $\frac{\left(3K\right)A(100-T)}{L}$

$=\frac{\left(2K\right)A(T-50)}{L}+\frac{\left(K\right)A\left(T\right)}{L}$

therefore $6T={4000}^{0C}$

$T=(\frac{200}{3}{)}^{0C}$