Question

Three identical rods $A$, $B$ and $C$ of equal lengths and equal diameters are joined in series as shown in the figure. Their thermal conductivities are $2K,K$ and $K/2$ respectively. Calculate the temperature at the two junction points :

• A. ${85.7}^{o}C,{57.1}^{o}C$
• B. ${80.85}^{o}C,{50.3}^{o}C$
• C. ${77.3}^{o}C,{48.3}^{o}C$
• D. ${75.8}^{o}C,{49.3}^{o}C$

Answer 1

The correct option is A ${85.7}^{o}C,{57.1}^{o}C$

$i_{th1}=i_{th2}=i_{th3}$

$\frac{(100-T_1)2KA}{l}=\frac{(T_1-T_2)KA}{l}=\frac{(T_1-0)KA}{2l}$

$\frac{(100-T_1)2KA}{l}=\frac{(T_1-0)KA}{2l}$

$T_1=85.7$

$\frac{(100-T_1)2KA}{l}=\frac{(T_1-T_2)KA}{l}$

$\frac{(100-85.7)2KA}{l}=\frac{(85.7-T_2)KA}{l}$

$T_2=57.1$