A partition wall has two layers of different materials A and B in contact with each other. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. At steady state the temperature difference across the layer B is 50 K, then the corresponding difference across the layer A is

Options

A. 50 k
B. 12.5 k
C. 25 k
D. 60 k

Answer

C

Explanation

Let T be the junction temperature
Here `K_(A) = 2K_(B) , T-T_(B) = 50 K`
At the steady state `H_(A) = H_(B)`
`implies (K_(A)A(T_(A)-T))/(L )=(K_(B)A(T-T_(B)))/(L)`
`implies 2K_(B)(T_(A)-T)=K_(B)(T-T_(B))`
`implies T_(A)-T= (T-T_(B))/(2) = (50)/(2) = 25 K`