Question

Two rectangular blocks A and B of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of A is 100°C and that of B at the other end is 0°C. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be

• A. 25°C
• B. 50°C
• C. 75°C
• D. 100°C

Answer 1

Answer: (A)

25°C

Answer 2

It is given that $\frac { K _ { 1 } } { K _ { 2 } } = \frac { 1 } { 3 }$ ⇒ $K _ { 1 } = K$ then $K _ { 2 } = 3 K$ the temperature of the junction in contact

$\theta = \frac { K _ { 1 } \theta _ { 1 } + K _ { 2 } \theta _ { 2 } } { K _ { 1 } + K _ { 2 } }$ $= \frac { 1 \times 100 + 3 \times 0 } { 1 + 3 } = \frac { 100 } { 4 }$= 25°C