A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be :

  • Option 1)

    225

  • Option 2)

    450

  • Option 3)

    1000

  • Option 4)

    1800

 

Answers (1)

As we learnt in

Radiant Power (P) -

P=frac{Q}{t}=Aepsilon sigma 	heta^{4}

-

 

 Power of radiation is 

P=\sigma A T^{4}    (For blackbody)

\frac{P_{2}}{P_{1}}=\left(\frac{A_{2}}{A_{1}} \right ).\left(\frac{T_{2}}{T_{1}} \right )^{4}=\left(\frac{r_{2}}{r_{1}} \right )^{2}.\left(\frac{T_{2}}{T_{1}} \right )^{4}

According to question

\frac{r_{2}}{r_{1}}=\frac{1}{2}\ \: \: \: and\ \: \: \: \frac{T_{2}}{T_{1}}=2

Then \frac{P_{2}}{P_{1}}=\left(\frac{1}{2} \right )^{2}.2^{4}=2^{2}

or P2 = 4P1 = 4 \times 450 W = 1800 W

Correct option is 4.

 


Option 1)

225

Incorrect

Option 2)

450

Incorrect

Option 3)

1000

Incorrect

Option 4)

1800

Correct

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