Heat loss takes place from a body maintained at a temperature of \(400^{\circ} \mathrm{C}\) to the surrounding air at \(30^{\circ} \mathrm{C}\) by convection and to the surrounding surfaces at \(30^{\circ} \mathrm{C}\) by radiation. The Newton's cooling coefficient is \(20 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}\) and the Stefan-Boltzmann constant is \(5.67 \times 10^{-8}\) \(\mathrm{W} / \mathrm{m}^2 \mathrm{~K}^4\). If the rate of heat loss by convection is equal to the rate of heat loss by radiation, the emissivity of the body surface is

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.