Question:

A black body emits heat at the rate of $20\, W$. When its temperature is $727^{\circ} C$. Another black body emits heat at the rate of $15\, W$, when its temperature is $227^{\circ} C$. Compare the area of the surface of the two bodies, if the surrounding is at NTP.

Updated On: Jul 2, 2022
  • $ 16:1 $
  • $ 1:4 $
  • $ 12:1 $
  • $ 1:12 $
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The Correct Option is D

Solution and Explanation

$\frac{P_{1}}{P_{2}}=\frac{\sigma A_{1} T_{1}^{2}}{\sigma A_{2} T_{2}^{2}}$ $\therefore \frac{A_{1}}{A_{2}} =\frac{P_{1}}{P_{2}} \times\left(\frac{T_{2}}{T_{1}}\right)^{4}$ $=\frac{20}{15}\left(\frac{500}{1000}\right)^{4}$ $=\frac{1}{12}$
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Concepts Used:

Heat Transfer

What is Heat Transfer?

It is defined as the movement of heat across the border of the system due to a difference in temperature between system and its surroundings.

How is Heat Transferred?

Heat can travel from one place to another in several ways. The different modes of heat transfer include:

  • Conduction - Heat flows from things with higher temp to objects with lower temp.
  • Convection - Movement of liquid molecules from higher temp regions to lower temp regions.
  • Radiation - Radiant heat is present in every other way in our daily lives. Thermal radiations are also known to as radiant heat. Thermal radiation is generated by the emission of electromagnetic waves.