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# Try this! 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 :

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

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As we learnt in

$P=\frac{Q}{t}=A\epsilon \sigma \theta^{4}$

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$P=\sigma A T^{4}$    (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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