Heat Transfer - Radiation: Practice Problem & Solution
Assertion (A): A sphere, a cube and a thin circular plate made of same material and of same mass are initially heated to \( 200^{\circ}\text{C} \), the plate will cool at fastest rate. Reason (R): Rate of cooling \( = \frac{\rho A \sigma}{ms} (T^4 - T_0^4) ) ( \propto \) surface area. Surface area is maximum for circular plate.
Solution Explained:
To solve this problem, we apply the core principles of Heat Transfer - Radiation. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is true because a thin plate has a larger surface area-to-mass ratio. Reason (R) states cooling rate \( \propto \) surface area, which is true \( \frac{dT}{dt} \propto \frac{A}{m}) \), and that a plate has the maximum surface area (for a given mass). Thus, both are true and (R) correctly explains (A).
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