Transmission Of Heat Question 209

Question: The temperature of a piece of iron is $ 27^{o}C $ and it is radiating energy at the rate of $ Q\ kW{{m}^{-2}} $ . If its temperature is raised to $ 151^{o}C $ , the rate of radiation of energy will become approximately

[MP PET 1992]

Options:

A) $ 2Q\ kW{{m}^{-2}} $

B) $ 4Q\ kW{{m}^{-2}} $

C) $ 6Q\ kW{{m}^{-2}} $

D) $ 8Q\ kW{{m}^{-2}} $

Show Answer

Answer:

Correct Answer: B

Solution:

$ E _{2}=E _{1}\frac{T _{2}^{4}}{T _{1}^{4}}=Q\times \frac{{{(273+151)}^{4}}}{{{(273+27)}^{4}}}={{( \frac{424}{300} )}^{4}}=3.99Q\approx 4Q $