A metal rod is placed between two temperature sources so that heat can flow between them. One temperature is 90.0 °C and the other temperature is 25.0 °C. The length of the rod is 30.0 cm and the cross-sectional area is 10.0 cm². If 15.0 watts of heat flows between the hot temperature and the cold temperature, then what is the thermal conductivity for the metal?

Question

Quizplus · Accepted Answer

The thermal conductivity ($k$) can be found using the formula for heat transfer: $Q = \frac{kA(T_{hot} - T_{cold})}{d}$, where $Q$ is the heat transfer rate (15.0 watts), $A$ is the cross-sectional area (10.0 cm^2 = 0.0010 m^2), $T_{hot}$ is the hot temperature (90.0 °C), $T_{cold}$ is the cold temperature (25.0 °C), and $d$ is the length of the rod (30.0 cm = 0.30 m). Rearranging the formula to solve for $k$ gives $k = \frac{Qd}{A(T_{hot} - T_{cold})}$. Plugging in the values gives $k = \frac{15.0 \times 0.30}{0.0010 \times (90.0 - 25.0)} = 69.2$ W/(m·°C).

A Metal Rod Is Placed Between Two Temperature Sources So