An aluminium rod of length `L` and cross-sectional area `2A` is joined with a copper rod of length `2L` and area of cross-section is `A` as shown in figure. Find the temperature of aluminium-copper junction in the steady state of the system.

Given thermal conductivity `K_(Al)=240J//m//s//.^(@)C, K_(Cu)=400J//m//s//.^(@)C`

Options

A. `300^(@)C`
B. `400^(@)C`
C. `288.24^(@)C`
D. `275.4^(@)C`

Explanation

(c) In steaky state condition rate of heat flow in both rods must be equal Let junction temperature `=T`
`H=Q/T=(K_(Al)A_(Al)(400^(@)-T))/(L_(Al))=(K_(Cu)A_(Cu)(T_20^(@)))/(L_(Cu))`
`=(240(2A)(400^(@)-T))/L=(400xxAxx(T-20^(@)))/(2L)`
`T=288.24^(@)C`