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 ______.

Options

• 25°C

• 50°C

• 75°C

• 100°C

Answer 1

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 25°C.

Explanation:

`R_A = L/(K_1a)`

`R_B = L/(K_2a)`

Where a is the cross sectional area of the rod and L is the length of the rod and K₁ and K₂ are the thermal conductivity of each rod.

`T_J = R_B/(R_A + R_B)(100 - 0)`

= `1/((R_A)/(R_B) + 1) xx 100`

= `100/(3 + 1)`

= 25°C