A cylindrical steel rod of length 0.10 m and thermal conductivity `50 W.m^(-1) K^(-1)` is welded end to end to copper rod of thermal conductivity `400 W.m^(-1). K^(-1)` and of the same area of cross section but 0.20 m long. The free end of the steel rod is maintained at `100^(@)C` and that of the copper and at `0^(@)C`. Assuming that the rods are perfectly insulated from the surrounding, the temperature at the junction of the two rods–

Options

A. `20^@C`
B. `30^@C`
C. `40^@C`
D. `50^@C`

Answer

A

Explanation

Resistance of steel

`(0.1)/(50 xx A)=(1)/(500A)`
Resistance of copper = `(0.2)/(400A)=(1)/(2000A)`
Both are connected in series hence heat current in both will be same.
So, `(100-T)/(((1)/(500A)))=(T-0)/(((1)/(2000A))) implies T=20^@C`