Question

Constants Part A You are asked to design a cylindrical steel rod 60.0 cm long, with a circular cross section, that will conduct 180.0 J/s from a furnace at 400.0 ° C to a container of boiling water under 1 atmosphere. What must the rod's diameter be? Express your answer with the appropriate units. D. Vale Unis D- Value Units

Answer 1

A)

L = length of the rod = 60 cm = 0.60 m

P = rate of heat transfer = 180 J/s

T_f = temperature of furnace = 400 ^oC

T_w = temperature of water = 100 ^oC

k = thermal conductivity of steel = 50.2 W/mK

A = area of cross-section = ?

Rate of heat transfer is given as

P = k A (T_f - T_w )/L

180 = (50.2) A (400 - 100)/0.60

A = 7.17 x 10^-3 m²

d = diameter

area is given as

A = (0.25) $\pi$d²

7.17 x 10^-3 = (0.25) (3.14) d²

d = 9.6 x 10^-2 m

d = 9.6 cm