A rod of negligible heat capacity has length 20 cm, cross-sectional area 1.0 cm² and thermal conductivity 200 W m⁻¹ °C⁻¹. One end is maintained at 0°C, while the other end is slowly and linearly raised from 0°C to 60°C in 10 minutes. Assuming no heat loss from the sides, find the total heat transmitted through the rod in these 10 minutes.
Physics · Thermodynamics
JEE Advanced

Question

A rod of negligible heat capacity has length 20 cm, cross-sectional area 1.0 cm² and thermal conductivity 200 W m⁻¹ °C⁻¹. One end is maintained at 0°C, while the other end is slowly and linearly raised from 0°C to 60°C in 10 minutes. Assuming no heat loss from the sides, find the total heat transmitted through the rod in these 10 minutes.

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 1800.