Help with assigment: Assume that both ends of the rod in Fig. 17.23a are maintained at a temperature of 0°C and that the initial temperature distribution along the rod is given by T = (100°C) sin πχ/L, where x is measured from the left end of the rod. The copper rod has length L = 0.100 m and cross-sectional area of 1.00 cm². a) Show the initial temperature distribution on a diagram. b) What is the final temperature distribution after a long time? c) Draw curves that, in your opinion, represent the temperature distribution at intermediate moments. d) Determine the initial temperature gradient at the ends of the rod. e) Calculate the initial heat flow from the ends of the rod to the bodies that are in contact with them. f) What initial heat flow is there in the center of the rod? Explain. What heat current is there at this point at a later instant? g) What is the value of the thermal diffusivity k/pc of copper, and in what unit is it expressed? (Here, k is the thermal conductivity, p = 8.9 × 103 kg/m³ is the density, and c is the specific heat). h) What is the initial rate of change of temperature in the center of the rod? i) How long would it take for the center of the rod to reach its final temperature if the temperature continues to decrease at that rate? (This time is called the relaxation time of the rod). j) From the graphs in part c), could we expect that the rate of change of the temperature at the midpoint remains constant, increases or decreases as a function of time? k) Determine the initial speed of change of temperature at a point on the rod located 2.5 cm from its left end.
Book is sears and zemansky University Physics 13th edition
