A uniform copper rod of 50 cm length is insulated on the sides and has its ends exposed to ice and steam respectively. If there is a layer of water 1 mm thick at each end, the temperature gradient in ° C m - 1 in the bar is (assume that the thermal conductivity of copper is 400 W m - 1 K - 1 and water is 0 .4 W m - 1 K - 1 )

Step-by-step solution

Given, K c = 400   W   m - 1   K - 1 , K w = 0.4   W   m - 1   K - 1 θ 1 = 100   ° C ,   θ 2 = 0   ° C In steady-state, the flow of heat will be the same throughout the whole system K w A 100 - θ 10 - 3 = K c A θ - θ ′ 50 100 Or 100 - θ = K c K w × 10 - 3 × θ - θ ′ 0.5 = 400 0.4 × 10 - 3 × θ - θ ′ 0.5 100 - θ = 2 θ - θ ′ ( 100 − θ ) K w A 10 &