Three discs A, B and C having radii 2; m, 4; | vedclass

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(B) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is the Stefan-B

Vedclass · Accepted Answer

$Q_B$ is maximum

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(B) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.Since the discs are coated with carbon black,they act as black bodies $(\varepsilon = 1)$.The area of a disc is $A = \pi r^2$,so $P \propto r^2 T^4$.According to Wien's displacement law,$\lambda_m T = b$ (constant),which implies $T \propto \frac{1}{\lambda_m}$.Substituting this into the power equation: $P \propto r^2 \left(\frac{1}{\lambda_m}ight)^4 = \frac{r^2}{\lambda_m^4}$.Now,calculating the relative values for $Q_A, Q_B,$ and $Q_C$:$Q_A \propto \frac{2^2}{300^4} = \frac{4}{81 	imes 10^8} \approx 0.049 	imes 10^{-8}$$Q_B \propto \frac{4^2}{400^4} = \frac{16}{256 	imes 10^8} = 0.0625 	imes 10^{-8}$$Q_C \propto \frac{6^2}{500^4} = \frac{36}{625 	imes 10^8} \approx 0.0576 	imes 10^{-8}$Comparing these values,$Q_B$ is the maximum.

Column-$I$	Column-$II$
$(a)$ Cup of hot tea in room	$(i)$ Forced convection
$(b)$ Substance kept near fire	$(ii)$ Natural convection
	$(iii)$ Conduction
	$(iv)$ Radiation

Similar Questions

In Column-$I$,system surroundings and in Column-$II$ modes of heat transfer are given below. Match the following:

Column-$I$ Column-$II$

$(a)$ Cup of hot tea in room $(i)$ Forced convection

$(b)$ Substance kept near fire $(ii)$ Natural convection

$(iii)$ Conduction

$(iv)$ Radiation

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In Column-$I$,system surroundings and in Column-$II$ modes of heat transfer are given below. Match the following: Column-$I$ Column-$II$ $(a)$ Cup of hot tea in room $(i)$ Forced convection $(b)$ Substance kept near fire $(ii)$ Natural convection $(iii)$ Conduction $(iv)$ Radiation

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In Column-$I$,system surroundings and in Column-$II$ modes of heat transfer are given below. Match the following:

Column-$I$ Column-$II$

$(a)$ Cup of hot tea in room $(i)$ Forced convection

$(b)$ Substance kept near fire $(ii)$ Natural convection

$(iii)$ Conduction

$(iv)$ Radiation