2. Two bars are conducting heat from a region of higher temperature to a region of lower temperature. The bars have identical
lengths and cross-sectional areas, but are made from different materials. In the drawing they are placed “in parallel” between
the two temperature regions in arrangement A, whereas they are placed end to end in arrangement B. In which arrangement is
the
heat
that
is
conducted
the
greatest?
(a) The heat conducted is the same in both arrangements. (b) Arrangement A (c) Arrangement B (d) It is not possible to
determine which arrangement conducts more heat.
4. The drawing shows a composite slab consisting of three materials through which heat is conducted from left to right. The
materials have identical thicknesses and cross-sectional areas. Rank the materials according to their thermal conductivities,
largest first. (a) k1, k2, k3 (b) k1, k3, k2 (c) k2, k1, k3 (d) k2, k3, k1 (e) k3, k2, k1
6. The long single bar on the left in the drawing has a thermal conductivity of 240 J/(s  m 2  C). The ends of the bar are at
temperatures of 400 and 200 C, and the temperature of its midpoint is halfway between these two temperatures, or 300 C.
The two bars on the right are half as long as the bar on the left, and the thermal conductivities of these bars are different (see
the drawing). All of the bars have the same cross-sectional area. What can be said about the temperature at the point where the
two bars on the right are joined together? (a) The temperature at the point where the two bars are joined together is
300 C. (b) The temperature at the point where the two bars are joined together is greater than 300 C. (c) The temperature at
the point where the two bars are joined together is less than 300 C.
* 13. ssm Three building materials, plasterboard [k = 0.30 J/(smC°)], brick [k = 0.60 J/(smC°)], and wood [k = 0.10 J/(smC°)],
are sandwiched together as the drawing illustrates. The temperatures at the inside and outside surfaces are 27C and 0C,
respectively. Each material has the same thickness and cross-sectional area. Find the temperature (a) at the plasterboard–brick
interface and (b) at the brick–wood interface.
*16. Multiple-Concept Example 3 discusses an approach to problems such as this. The ends of a thin bar are maintained at
different temperatures. The temperature of the cooler end is 11C, while the temperature at a point 0.13 m from the cooler end
is 23C and the temperature of the warmer end is 48C. Assuming that heat flows only along the length of the bar (the sides are
insulated), find the length of the bar.
** 18. The drawing shows a solid cylindrical rod made from a center cylinder of lead and an outer concentric jacket of copper.
Except for its ends, the rod is insulated (not shown), so that the loss of heat from the curved surface is negligible. When a
temperature difference is maintained between its ends, this rod conducts one-half the amount of heat that it would conduct if it
were solid copper. Determine the ratio of the radii r1/r2.
** 19. ssm www Two cylindrical rods have the same mass. One is made of silver (density 10 500 kg/m3), and one is made of iron
(density 7860 kg/m3). Both rods conduct the same amount of heat per second when the same temperature difference is
maintained across their ends. What is the ratio (silver-to-iron) of (a) the lengths and (b) the radii of these rods?
*32. Part (a) of the drawing shows a rectangular bar whose dimensions are L0 x 2L0 x 3L0. The bar is at the same constant
temperature as the room (not shown) in which it is located. The bar is then cut, lengthwise, into two identical pieces, as shown
in part (b) of the drawing. The temperature of each piece is the same as that of the original bar. (a) What is the ratio of the
power absorbed by the two bars in part (b) of the drawing to the single bar in part (a)? (b) Suppose that the temperature of the
single bar in part (a) is 450.0 K. What would the temperature (in kelvins) of the room and the two bars in part (b) have to be so
that the two bars absorb the same power as the single bar in part (a)?
** 33. ssm A solid cylinder is radiating power. It has a length that is ten times its radius. It is cut into a number of smaller
cylinders, each of which has the same length. Each small cylinder has the same temperature as the original cylinder. The total
radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there?
**44. A small sphere (emissivity = 0.90, radius = r1) is located at the center of a spherical asbestos shell (thickness = 1.0 cm,
outer radius = r2). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the
small sphere is 800.0 C, while the temperature of the inner surface of the shell is 600.0 C, both temperatures remaining
constant. Assuming that r2/r1 = 10.0 and ignoring any air inside the shell, find the temperature of the outer surface of the shell.