How different would the rate of heat transfer from a hot reservoir to a cold reservoir be if one uses a 10-cm glass rod instead of a 10-m long aluminum rod having identical cross sectional areas?

Question

Quizplus · Accepted Answer

The rate of heat transfer is given by the formula Q/t = kA(T1-T2)/L, where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area, T1 and T2 are the temperatures of the hot and cold reservoirs respectively, and L is the length of the rod. Since the cross-sectional areas of the glass and aluminum rods are identical, we can simplify the formula as Q/t = k(T1-T2)/L. The thermal conductivity of aluminum is much higher than that of glass, which means the rate of heat transfer is much faster in aluminum than in glass. Therefore, using a 10-cm glass rod instead of a 10-m long aluminum rod would slow down the rate of heat transfer by a factor of (10m / 10cm) x (k_aluminum / k_glass) = 100 x (205 W/m*K / 1.05 W/m*K) = 19619, which is approximately 2.75 times slower.

How Different Would the Rate of Heat Transfer from a Hot