B

Step 1: Convert the surface area from cm² to m².

• 1 cm² = 1 × 10^{-4} m², so
• 5.00 cm² = 5.00 × 10^{-4} m².

Step 2: Convert temperature from Celsius to Kelvin.

• Temperature in Kelvin (K) = Temperature in Celsius + 273.15, so
• 727 ºC = 727 + 273.15 = 1000.15 K ≈ 1000 K.

Step 3: Calculate the power radiated by the body.

• Energy radiated per minute = 300 J.
• Power (P) = Energy/time = 300 J/60 s = 5 W.

Step 4: Use the Stefan-Boltzmann law to find emissivity (ε).
The Stefan-Boltzmann law is given by:
$$ P = εσAT^4 $$
Where:

• ε is the emissivity
• σ (Stefan-Boltzmann constant) = 5.67 × 10^{-8} W/m²K⁴
• A = 5.00 × 10^{-4} m²
• T = 1000 K

Step 5: Substitute the values into the equation:

• 5 W = ε × (5.67 × 10^{-8} W/m²K⁴) × (5.00 × 10^{-4} m²) × (1000 K)⁴

Step 6: Calculate T⁴:
$$ T^4 = (1000 K)^4 = 10^{12} K^4 $$
Step 7: Substitute T⁴ into the equation:
$$ 5 = ε × (5.67 × 10^{-8}) × (5.00 × 10^{-4}) × (10^{12}) $$
Step 8: Simplify:
$$ 5 = ε × (5.67 × 5.00) × 10^{4} $$
$$ 5 = ε × (28.35 × 10^{4}) $$
Step 9: Solve for ε:
$$ ε = \frac{5}{28.35 × 10^{4}} $$
$$ ε ≈ \frac{5}{2835000} ≈ 0.00000176 $$
Step 10: Since emissivity (ε) value must be between 0 and 1, round it properly if necessary. Thus, in appropriate format, Answer: Emissivity ε ≈ 0.00000176, which matches Option B.