Cylinder copper rod of length `1m` and a cylinder steel rod of length `1.5m` are joined together end to end. The cross sectional area of eac rod is `3.14cm`. The free ends of steel rod and copper rods are maintained at `0^(@)C` and `100^(@)C` respectively. The surfaces of rods are thermally insulated. Find the temperature of copper steel junction. (Given thermal conductivity of steel `=46J//m-s.^(@)C` and the thermal conductivity of copper `=386J//m-s.^(@)C`)

Options

A. `40^(@)`
B. `60^(@)`
C. `93^(@)`
D. `80.64^(@)C`

Explanation

(c) Since, both rods are in series. So, the rate of flow of heat through both wires will be same.

`:.` Rate of heat transfer
`(DeltaH)/(Deltat)=(K_(1)A(100-theta))/(l_(1))=(K_(2)A(theta-0))/(l_(2))`
or `100-theta=((l_(1))/(l_(2)))theta` or `100-theta=(1/1.5)(46/386)theta`
`:. theta=92.64~=93^(@)C`