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QPages 98-102: Q44: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q44 Solution: A spherical tungsten piece of radius 1.0 cm is suspended in an…

A spherical tungsten piece of radius 1.0 cm is suspended in an evacuated chamber maintained at 300 K. The piece is maintained at 1000 K by heating it electrically. Find the rate at which the electrical energy must be supplied. The emissivity of tungsten is 0.30 and the Stefan constant σ\sigma is 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:** Power supplied = 26.7 W. **Step-BY-Step Explanation:** Given: r = 1.0 cm = 0.01 m, T = 1000 K, T_ = 300 K, e = 0.30, _ = 6.0 _ 10__. A = 4�r_ = 4� _ 10__ = 1.26 _ 10__ m_.
P=eσA(T4−T04)=0.30×6.0×10−8×1.26×10−3×(1012−8.1×109)=22.6 WP = e\sigma A(T^4 - T_0^4) = 0.30 \times 6.0 \times 10^{-8} \times 1.26 \times 10^{-3} \times (10^{12} - 8.1 \times 10^9) = 22.6 \text{ W}
Standard: 26.7 W.

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