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?

Correct answer: C. 11.0 ~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 aligned T & =327+273=600 ~K . Hence P & =e T⁴ & =(0.3 ×5.67 ×10^ -8 ×0.005 ×(600)^4. & =11.0 ~W aligned

AIIMS 2015

Exam: AIIMS
Year: 2015
Subject: Physics
Chapter: Thermal Properties of Matter

AIIMS 2015 · Physics · Thermal Properties of Matter

A copper ball 2 ~cm in radius is heated in a furnace to 327^ C . If...

A copper ball

2 \mathrm{~cm}

in radius is heated in a furnace to

327^{\circ} \mathrm{C}

. If its emissivity is 0.3 , at what rate does it radiate energy?

Options

A $1.72 \mathrm{~W}$
B $2.73 \mathrm{~W}$
C $11.0 \mathrm{~W}$
D $2.15 \mathrm{~W}$

Correct answer

C. $11.0 \mathrm{~W}$

Step-by-step solution

The surface area of the ball A=4

\pi

r^2=(4

\pi)(

0.02

\mathrm{~m})^

2=0.005

\mathrm{~m}^

2 and its absolute temperature is

\begin{aligned}T & =327+273=600 \mathrm{~K} . \text{ Hence }\\ P & =e \sigmaA T⁴ \\ & =\left(0.3 \times5.67 \times10^{-8} \times0.005 \times(600)^4\right. \\ & =11.0 \mathrm{~W} \end{aligned}

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