One end of copper rod of uniform cross-section and of length 1.5 meters is in contact with melting ice and the other end with boiling water. At what point along its length should a temperature of 200°C be maintained, so that in steady state, the mass of ice melting is equal to that of steam produced in the same interval of time? Assume that the whole system is insulated from the surroundings.
Physics · Thermodynamics
JEE Advanced

Question

One end of copper rod of uniform cross-section and of length 1.5 meters is in contact with melting ice and the other end with boiling water. At what point along its length should a temperature of 200°C be maintained, so that in steady state, the mass of ice melting is equal to that of steam produced in the same interval of time? Assume that the whole system is insulated from the surroundings.

Physics · Thermodynamics

G1 Physics · Accepted Answer

In steady conduction, heat current is H=kAΔT/L. Treat each segment as a thermal resistance Rₜₕ=L/(kA); series resistances add and parallel heat currents add. Substituting the given values gives 10.34.