Suppose that the rod in Fig. 17.24a is made of copper, is 45.0 cm long, and has a cross-sectional area of 1.25 cm2. Let TH = 100.0°C and TC = 0.0°C. (a) What is the final steady-state temperature gradient along the rod? (b) What is the heat current in the rod in the final steady state? (c) What is the final steady-state temperature at a point in the rod 12.0 cm from its left end?
Question
Answer: a) 222k/m
b) 42.5W
c) if cold: 26.7C
If hot: 73.3C
Explanation:
If TH and TC are at the ends of the rod in the figure, then;
(A) 100 K / 45 cm = 2.22 K/cm or 222 K/m
(B) thermal conductivity constant for copper is 390 W/(m K).
Then the heat flow rate = Q/t
Q/t = [390 W/(m K)] (100 K) [ pi (0.0125 m)^2 ] / (0.45 m)
= 42.5 watts
(C) 12/45 = 4/15 = 0.2667
If the left end is the cold end, the answer will be 26.7 C
If the left end is the hot end, the answer will be 73.3 C