Question

One end of an insulated metal rod is maintained at 100 ∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. The rod has a length of 50.0 cm and a cross-sectional area of 1.20 cm2 . The heat conducted by the rod melts a mass of 9.00 g of ice in a time of 10.0 min .

Part A

Find the thermal conductivity k of the metal.

k =

W/(m⋅K)

Answer 1

Latent heat of fusion of water = L = 334000 J

Mass of ice melted in 10 min = m = 9 g = 0.009 kg

Heat removed from the ice = H

H = mL

H = (0.009)(334000)

H = 3006 J

Time period = t = 10 min = 10 x (60) sec = 600 sec

Rate at which heat is conducted through the rod = Q

H = Qt

3006 = Q(600)

Q = 5.01 W

Thermal conductivity of the metal = k

Length of the rod = L = 50 cm = 0.5 m

Cross-sectional area of the rod = A = 1.2 cm² = 1.2 x 10^-4 m²

Temperature of one end of the rod = T₁ = 0 ^oC

Temperature of the other end of the rod = T₂ = 100 ^oC

k = 208.75 W/(m.K)

Thermal conductivity of the metal = 208.75 W/(m.K)