Question

A baseball of radius r = 5.2 cm is at room temperature T = 20.8 C. The baseball has emissivity of ε = 0.86 and the Stefan-Boltzman constant is σ = 5.67 × 10-8 J/(s⋅m2⋅K4). Say this ball is now moved to a region approximating T=0 K (space, for instance). P = 4πεσr2T4. What is the power in W? Numeric : A numeric value is expected and not an expression. P = __________________________________________

Answer 1

Stefan-Boltzman constant = = 5.67 x 10^-8 J/(s.m².K⁴)

Radius of the baseball = R = 5.2 cm = 0.052 m

Surface area of the baseball = A = 4R²

Temperature of the baseball = T = 20.8 ^oC = 20.8 + 273 K = 293.8 K

Emissivity of the baseball = = 0.86

Power emitted by the baseball = P

P = AT⁴

P = 4R²T⁴

P = 4(0.86)(5.67x10^-8)(0.052)²(293.8)⁴

P = 12.35 W

Power emitted by the baseball = 12.35 W