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QPages 98-102: Q43: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q43 Solution: A spherical ball of surface area absorbs any radiation that…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often replace the $T^4$ dependence in the Stefan‑Boltzmann law with a linear $T$ or a simple difference $T_{ball}-T_{box}$, yielding $P=\sigma A(T_{ball}-T_{box})$ instead of the correct $P=\sigma A(T_{ball}^4-T_{box}^4)$. Always keep temperatures in Kelvin and apply the fourth‑power term when computing emitted or absorbed radiation.

A spherical ball of surface area 20 cm220 \text{ cm}^2 absorbs any radiation that falls on it. It is suspended in a closed box maintained at 57�C. a) Find the amount of radiation falling on the ball per second. b) Find the net rate of heat flow to or from the ball at an instant when its temperature is 200�C. Stefan constant = 6.0×10−8 W m−2 K−46.0 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}.

Step-by-Step Verified Solution

**Answer:** (a) 0.48 W (b) 1.9 W net loss. **Step-BY-Step Explanation:** Given: A = 20 cm_ = 20 _ 10__ m_, T_box = 57�C = 330 K, T_ball = 200�C = 473 K, _ = 6.0 _ 10__. (a) Radiation falling = _A T_box_ = 6.0 _ 10__ _ 20 _ 10__ _ (330)_ = 0.48 W. (b) Net loss = _A(T_ball_ _ T_box_) = 6.0 _ 10__ _ 20 _ 10__ _ (473_ _ 330_) = 1.9 W.

All Questions in this Chapter

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