Question

24. Two metal cubes X and Y of same size are
arranged as shown in figure. The extreme ends of the combination are maintained at the indicated temperatures. The given arrangement is thermally insulated. The
coefficient of thermal conductivity of X and Y are 300 W/m°C and 200 W/m°C
respectively. What will be the temperature (T) of the interface in the steady state?​

Answer 1

The temperature in the steady state will be 60°C.

Conductivity of X = 300 W/m°C (GIven)

Conductivity of Y = 200 W/m°C (GIven)

Heat temperature though A per second will be -  

Q1 = K1A (100−t) / l  

Heat transferred through B per second will be -  

Q2 = K2A (t−0) / l  

At the steady state, the temperature will be -

= K1A(100−t) / l = K2A (t−0)/l  

= 300 (100−t) = 200 (t−0)  

= 300−3t =2t

= 60°C