A copper ball 2 cm in radius is heated in a furnace to 327 °C. If its emissivity is 0.3, at what rate does it radiate energy?

Question

A copper ball 2 cm in radius is heated in a furnace to 327 °C. If its emissivity is 0.3, at what rate does it radiate energy? (A) 1.72 W (B) 2.73 W (C) 11.0 W (D) 2.15 W

Tardigrade Admin · Accepted Answer

The surface area of the ball A=4 π r2=(4 π)(0.02 m )2=0.005 m 2 and its absolute temperature is T =327+273=600 K . Hence P =e σ AT 4 =(0.3 × 5.67 × 10-8 × 0.005 ×(600)4. =11.0 W

Q. A copper ball $2 c m$ in radius is heated in a furnace to $327^{\circ}$ C. If its emissivity is $0.3$ , at what rate does it radiate energy?

1.72 W

2.73 W

11.0 W

2.15 W

The surface area of the ball
$A = 4 π r^{2} = (4 π) (0.02 m)^{2} = 0.005 m^{2}$
and its absolute temperature is
$T = 327 + 273 = 600 K .$ Hence
$P = e σ A T^{4}$
$= (0.3 \times 5.67 \times 1 0^{- 8} \times 0.005 \times (600)^{4}$
$= 11.0 W$

Q. A copper ball 2cm in radius is heated in a furnace to 327∘C. If its emissivity is 0.3, at what rate does it radiate energy?