Question

1) A copper rod and an aluminium rod of the same length and cross-sectional area are attached end to end. The copper end is placed in a furnace maintained at a constant temperature of 272°C. The aluminium end is placed in an ice bath held at a constant temperature of 0.00°C.

Calculate the temperature at the point where the two rods are joined. 

 

Answer 1

Answer:-

thermal conductivity of copper and aluminium are respectively 380 and 200 W/m/◦ C.

Temperature of hot end

-from the information

$\frac{\Delta Q}{\Delta t}=\frac{KA_lT}{L}=P$

in steady state

$Q_{cu}loss=Q_{al}Gained$

$P_{al}=-P_{cu}$

$\frac{KA_LA_{AL}\Delta T_{AL}}{L_{AL}}=\frac{-K_{cu}A_{cu}\Delta T_{cu}}{L_{cu}}$

But

$L_{AL}=L_{cu}=L$

$A_{AL}=A_{cu}=A$

$\frac{K_{AL}A\Delta T_{AL}}{L}=\frac{-K_{cu}A\Delta T_{CU}}{L}$

$K_{AL}\Delta T_{AL}=-K{cu}\Delta _{cu}$

$K_{AL}(T-T_C)=-K_{cu}(T-T_H)$

$k_{AL}T=-K_{CU}T+K_{cu}(T_H)$

$T(k_{AL}+K_{cu})=K_{cu}T_H$

$T=\frac{K_{cu}T_H}{(K_{AL}+K_{cu})}$

$T=\frac{380\times200}{380+200}$

$\boxed{T=131.034 ^oC}$