The answer is (D) 2637 Watts.

Refer to page 116 of the FE Handbook: Heat Transfer, Radiation:

The radiation emitted by a body is given by:

Q = ε• σ •A•T4

Given:

ε = .7

σ = 5.67 × 10-8 W / (m2•K4) (the Stefan-Boltzmann constant)

A = 1 m2 (not given, however, the problem statement says per square meter, so just use 1 m2)

T = Temperatures must be in absolute temperatures (ºR or K)

Using page 1 of the FE Handbook : Temperature Conversion:

Since the problem statement gives us the temperature in ºC, it’s easy to convert to K.

K = ºC + 273.15

TL:

K = 30 + 273.15

K = 303.15

TH:

K = 250 + 273.15

K = 523.15

Therefore:

Q = ε• σ •A•T4

Q = (.7) • (5.67 × 10-8 W / (m2•K4)) • 1 m2 • (523.154 K4 – 303.154 K4)

Q = (.7) • (5.67 × 10-8 W / (m2•K4)) • 1 m2 • (66,458,388,419.2K4)

Q = 2637 Watts

The answer is (D) 2637 Watts.