The ends of a copper rod of length 1m and area of cross-section `1cm^2` are maintained at `0^@C` and `100^@C`. At the centre of the rod there is a source of heat of power 25 W. Calculate the temperature gradient in the two halves of the rod in steady state. Thermal conductivity of copper is `400 Wm^-1 K^-1`.

Explanation

Net thermal current supplied by source `((DeltaQ)/(Deltat))` then
`(DeltaQ)/(Deltat)=(DeltaQ_(1))/(Deltat)+(DeltaQ_(2))/(Deltat)`
`25=(kA)/(0.5)(T-100)+(kA)/(0.5)(T-0)`
`(25xx0.5)/(400xx1xx10^(-4))=2T-100`
`:. 2T=(1250)/(4)+100`
`T=206.25^(@)C`