AP EAMCET · PHYSICS · Thermal Properties of Matter

A sphere of surface area $4 m^{2}$ at temperature $400 K$ and having emissivity $0.5$ is located in an environment of temperature $200 K$ . The net rate of energy exchange of the sphere is (Stefan Boltzmann constant $σ = 5.67 \times 10^{- 8} W m^{- 2} K^{4}$ )

A $3260.8 W$
B $1632.4 W$
C $2721.6 W$
D $4216.4 W$

Verified Solution

Answer & Solution

Correct Answer

(C) $2721.6 W$

Step-by-step Solution

Detailed explanation

The net rate of energy exchange of the sphere is, P=εσAT4-Ts4. Given: ε=0.5 σ=5.67×10-8 W m-2 K4 A=4 m2 T=400 K and Ts=200 K Therefore, P=0.5×5.67×10-8×44004-2004=2721.6 W

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A sphere of surface area 4 m2 at temperature 400 K and having emissivity 0.5 is located in an environment of temperature 200 K. The net rate of energy exchange of the sphere is (Stefan Boltzmann constant σ=5.67×10-8 W m-2 K4)

Step-by-step Solution

A sphere of surface area $4 m^{2}$ at temperature $400 K$ and having emissivity $0.5$ is located in an environment of temperature $200 K$ . The net rate of energy exchange of the sphere is (Stefan Boltzmann constant $σ = 5.67 \times 10^{- 8} W m^{- 2} K^{4}$ )