Question

Two bars of equal length and the same cross-sectional area but of different thermal conductivities, k₁ and k₂, are joined end to end as shown in figure. One end of the composite bar is maintained at temperature T_h where as the opposite end is held at T_c. If there are no heat losses from the sides of the bars, the temperature T_j of the junction is given by –

• A. $\frac { \mathrm { k } _ { 2 } } { \mathrm { k } _ { 1 } }$ $\frac{(T_{h} + T_{c})}{2}$
• B. $\frac{k_{2}}{k_{1} + k_{2}}$ (T_h + T_c)
• C. $\frac{(T_{h} + T_{c})}{2}$
• D. $\frac{1}{k_{1} + k_{2}}$ (k₁T_h + k₂T_c)

Answer 1

Answer: (D)

$\frac{1}{k_{1} + k_{2}}$ (k₁T_h + k₂T_c)

Answer 2

t µ $\frac{Kr^{2}}{\mathcal{l}}$

t₁ = t₂

$\frac{K_{1}r_{1}^{2}}{\mathcal{l}_{1}}$= $\frac{K_{2}r_{2}^{2}}{\mathcal{l}_{2}}$