Question

A silver bar of length 30 cm and cross sectional area 4.0 cm2 is used to transfer heat from a 100°C reservoir to a 0°C block of ice. How much ice is melted per second? (For silver, k = 427 J/s·m·°C. For ice, Lf = 334 000 J/kg.)

Question 20 options: 0.42 g/s 0.21 g/s 0.17 g/s 0.12 g/s

Answer 1

Thermal conductivity of silver = K = 427 J/(m.s.^oC)

Length of the silver bar = L = 30 cm = 0.3 m

Cross-sectional area of the silver bar = A = 4 cm² = 4 x 10^-4 m²

Temperature of one end of the silver bar = T₁ = 100 ^oC

Temperature of the other end of the silver bar = T₂ = 0 ^oC

Rate of heat transfer through the silver bar = Q

Q = 56.93 J/s

Mass of ice melted per second = m

Latent heat of fusion for ice = L = 334000 J/kg

Q = mL

56.93 = m(334000)

m = 1.7 x 10^-4 kg/s

m = 0.17 g/s

Ice melting per second = 0.17 g/s