KVPY SX SB Exam 2012 Question Paper

Question : 91 of 120

Marks: +1, -0

PHYSICS

The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from 10.0 °C to 11.0°C. The absolute temperature of the black body is doubled and its surface area halved and the experiment repeated for tire same time. Which of the following statements would be most nearly correct?

The temperature of the water would increase from 10.0°C to a final temperature of 12°C
The temperature of the water would increase from 10.0°C to a final temperature of 18°C
The temperature of the water would increase from 10.0°C to a final temperature of 14°C
The temperature of the water would increase from 10.0°C to a final temperature of 11°C

Validate

Solution:

Energy radiated,

\U∝ \AT ^4t

⇒\U_1/\U_2={\A\/2(2\T)^4 .t}/{\AT^4 .t}=8

⇒\U_2=8\U_1

⇒\mS\Δt_2=8\mS\Δt_1

⇒\Δt_2=8\Δt_1

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