How would the rate of heat transfer between a thermal reservoir at a higher temperature and one at a lower temperature differ if the reservoirs were in contact with a 10 -cm-long glass rod instead of a 10 -m-long aluminum rod having an identical cross-sectional area?

We need to use the formula for heat transfer through conduction. The formula is given by: Q = (k * A * (Th - Tc) * t) / L Where Q is the heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area, Th is the higher temperature, Tc is the lower temperature, t is the time period for which the heat transfer occurs, and L is the length of the rod. In this exercise, we are concerned with comparing heat transfer rates (Q/t). Therefore, we can simplify the formula as follows: Q/t = (k * A * (Th - Tc)) / L

We need to know the thermal conductivities of glass and aluminum to calculate the heat transfer rates. The general values for the thermal conductivities are: k_glass ≈ 0.8 W/(m·K) k_aluminum ≈ 205 W/(m·K)

Let's denote the heat transfer rates of glass and aluminum rods as Q/t_glass and Q/t_aluminum, respectively. To compare the heat transfer rates of the two rods, we can put the values from Step 2 into the simplified formula from Step 1: Q/t_glass = (k_glass * A * (Th - Tc)) / L_glass Q/t_aluminum = (k_aluminum * A * (Th - Tc)) / L_aluminum Given that the cross-sectional area (A), temperature difference (Th - Tc), and lengths of the rods (L_glass = L_aluminum = 10 cm = 0.1m) are identical, we can find the ratio of the heat transfer rates: (Q/t_glass) / (Q/t_aluminum) = k_glass / k_aluminum Plug in the values for the thermal conductivities: (Q/t_glass) / (Q/t_aluminum) = 0.8 / 205 = 0.0039 Therefore, the heat transfer rate of the glass rod is only about 0.39% (0.0039 * 100) of the aluminum rod. In conclusion, the rate of heat transfer between the thermal reservoirs would be significantly lower when using a glass rod compared to an aluminum rod, with the same cross-sectional area and length.