SATHEE: Heat and Thermodynamics 3 Question 30

Heat and Thermodynamics 3 Question 30

30. Two spherical bodies $A$ (radius $6 c m$ ) and $B$ (radius $18 c m$ ) are at temperatures $T_{1}$ and $T_{2}$ , respectively. The maximum intensity in the emission spectrum of $A$ is at $500 n m$ and in that of $B$ is at $1500 n m$ . Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$ ?

(2010)

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Answer:

Correct Answer: 30. 9

Solution:

$λ_{m} \propto \frac{1}{T}$

$∴ \frac{λ_{A}}{λ_{B}} = \frac{T_{B}}{T_{A}} = \frac{500}{1500} = \frac{1}{3}$

$E \propto T^{4} A$ (where, $A =$ surface area $= 4 π R^{2}$ )

$∴ E \propto T^{4} R^{2}$

$\frac{E_{A}}{E_{B}} = {(\frac{T_{A}}{T_{B}})}^{4} {(\frac{R_{A}}{R_{B}})}^{2} = (3)^{4} {(\frac{6}{18})}^{2} = 9$

$∴$ Answer is 9 .

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Heat and Thermodynamics 3 Question 30

Answer:

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