A black body at a temperature of 227^{circ}C | vedclass

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Question

(A) According to Stefan-Boltzmann Law,the rate of heat radiation per unit area $E$ is proportional to the fourth power of the absolute temperature $T$

Vedclass · Accepted Answer

$80$

Vedclass · Answer

(A) According to Stefan-Boltzmann Law,the rate of heat radiation per unit area $E$ is proportional to the fourth power of the absolute temperature $T$,i.e.,$E \propto T^4$.Given:$T_1 = 227^{\circ}C = 227 + 273 = 500 \ K$$E_1 = 5 \ cal/cm^2-sec$$T_2 = 727^{\circ}C = 727 + 273 = 1000 \ K$Using the ratio formula:$\frac{E_2}{E_1} = \left( \frac{T_2}{T_1} ight)^4$$\frac{E_2}{5} = \left( \frac{1000}{500} ight)^4$$\frac{E_2}{5} = (2)^4 = 16$$E_2 = 16 	imes 5 = 80 \ cal/cm^2-sec$.Thus,the correct option is $A$.

$A$ black body at a temperature of $227^{\circ}C$ radiates heat energy at the rate of $5 \ cal/cm^2-sec$. At a temperature of $727^{\circ}C$,the rate of heat radiated per unit area in $cal/cm^2-sec$ will be:

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