Question

A copper rod 85 cm long is used to poke a fire. The hot end of the rod is maintained at 115 °C and the cool end has a constant temperature of 22 °C. What is the temperature of the rod 25cm from the cool end?

Please provide a full explanation and formula and units throughout the calculations so that I can understand. Please type answer, no hand-written please.

Answer 1

L = length of the rod = 85 cm = 0.85 m

k = thermal conductivity

P = rate of heat transfer through the copper rod

A = area of cross-section

T_c = temperature of the cool end = 22 C

T_h = temperature of the hot end = 115 C

L_c = distance of the point from cool end = 25 cm = 0.25 m

T = temperature at distance 25 cm from cool end

L_h = distance of the point from hot end = 60 cm = 0.60 m

rate of heat transfer on left section AB = rate of heat transfer on right section BC

k A (T - 22)/L_c = k A (115 - T)/L_h

(T - 22)/L_c = (115 - T)/L_h

(T - 22)/0.25 = (115 - T)/0.60

T = 49.4 C