Question

Two pots are identical except that the flat bottom of one is aluminum, whereas that of the other is copper. Water in these pots is boiling away at 100.0 ˚C at the same rate. The temperature of the heating element on which the aluminum bottom is sitting is 156 ˚C. Assume that heat enters the water only through the bottoms of the pots and find the temperature of the heating element on which the copper bottom rests.

Answer 1

the rate of boiling is same. So both are taking heat at the same rate (Q-dot = joule/sec) through the process of conduction. Both same area of crossection (A) and thickness(x). their conduction heat equations are: (c-copper, a-allumi let the heating element of copper be at {t oC) qc-dot = kc A [tc - 100] / x qa-dot = ka A [150 - 100] / x given rates of Q are same, qc-dot = qa-dot kc A [tc - 100] / x = ka A [150 - 100] / x [tc - 100] = [ka/kc] [50] tc = 100 + [ka/kc] [50] ------------------------------------ ka = 237 W/m C kc= 401 W/m C http://en.wikipedia.org/wiki/Thermal_gre... ------------------------------ tc = 100 + [237/401] [50] tc = 129.55 0 C copper pot heating element is 129.55 C higer conductivity material would require low input temp source. k * t = const (if Q is same) t = const / k >> metal with higher k will have lower source temp