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Two rods, one made of copper and the oth...

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) ?

A

`12^@C`

B

`50^@C`

C

`73^@C`

D

`88^@C`

Text Solution

Verified by Experts

The correct Answer is:
D
`(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`.
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