Two rods, one made of copper and the other steel of the same length and cross sectional area are joined together. (The thermal conductivity of copper is `385 J.s^(-1) .m^(-1). K^(-1)` and steel is `50 J.s^(-1).m-^(1).K^(-1)`.) If the copper end is held at `100^(@)C` and the steel end is held at `0^(@)C`, what is the junction temperature (assuming no other heat losses) ?

Options

A. `12^@C`
B. `50^@C`
C. `73^@C`
D. `88^@C`

Answer

D

Explanation

`(100-T)/(R_1)=(T-0)/(R_2) implies (100-T)/(T)=(R_1)/(R_2)`
`R=(L)/(kA) implies (R_1)/(R_2)=(k_2)/(k_1)`
`(100-T)/(T)=(50)/(385)=(10)/(77)`
`implies 7700-77T=10T implies T=(7700)/(87)=88^@C`.