A sphere 15 cm in diameter is covered with 5 cm of insulation (k = 0.057 kcal/m-hr-°C). The inside and outside surface temperature of the insulation are 315°C and 80°C respectively. The heat loss per sq. m of the outside surface will be closer to

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Quizplus · Accepted Answer

The heat loss through a spherical shell can be calculated using the formula $Q = \frac{4\pi k (T_1 - T_2)r_1r_2}{r_2 - r_1}$, where $Q$ is the heat loss per hour, $k$ is the thermal conductivity, $T_1$ and $T_2$ are the inside and outside temperatures respectively, and $r_1$ and $r_2$ are the inside and outside radii of the spherical shell. Given $k = 0.057 \, \text{kcal/m-hr-°C}$, $T_1 = 315°C$, $T_2 = 80°C$, $r_1 = 7.5 \, \text{cm} = 0.075 \, \text{m}$, and $r_2 = 12.5 \, \text{cm} = 0.125 \, \text{m}$, substituting these values into the formula gives the heat loss. To find the heat loss per square meter of the outside surface, divide $Q$ by the outside surface area, $4\pi r_2^2$. However, the calculation provided directly aims for the heat loss without requiring division by the outside area, as the formula already accounts for the geometry. The correct answer involves calculating with the given values, leading to an approximation of the heat loss rate, which is closest to 160 kcal/hr, considering the spherical geometry and the thermal properties provided.

A Sphere 15 Cm in Diameter Is Covered with 5