?A copper bar 2.5 m long has a circular cross section of radius 2 cm. One end is

Question

?A copper bar 2.5 m long has a circular cross section of radius 2 cm. One end is kept at 80 oC? and the other end is kept at 0 oC. The surface of the bar is insulated so that there is negligible heat loss through it. If kcopper = 401 W.m-1.K-1, (a) what is the temperature of the rod 1.2 m from the hot end? (b) What is the thermal resistance of the bar? (c) What is the temperature of the bar 25 cm from the hot end?

Explanation / Answer

A copper bar 2.5 m long has a circular cross section of radius 2 cm. One end is kept at 80oC and the other end is kept at 0oC. The surface of the bar is insulated so that there is negligible heat loss through it. If kcopper = 401 Wm-1K-1, what is the temperature of the bar 25 cm from the hot end? under steady state, heat flow rate = same through all sections Q = watt = - k A [80 - 0] / [0 - 2.5] ................. entire rod ====================== let temperature at section 0.25 m away = t for given length Q1 = watt = - k A [80 - t] / [0 - 0.25] ============================= steady state > Q = Q1 [80 - t] / [0 - 0.25] = [80 - 0] / [0 - 2.5] ---------------------------- temperature gradients are equal [80 - t]/0.25 = 80/2.5 80 - t = 8 t = 72 deg C

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