The spectrum of a black body at two temperatu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the Stefan-Boltzmann law,the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of

Vedclass · Accepted Answer

$16 : 1$

Vedclass · Answer

(A) According to the Stefan-Boltzmann law,the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature $(E \propto T^4)$.The area under the intensity-wavelength curve represents the total emissive power of the black body at that temperature.Therefore,the ratio of the areas $A_1$ and $A_2$ corresponding to temperatures $T_1$ and $T_2$ is given by $\frac{A_2}{A_1} = \frac{T_2^4}{T_1^4}$.Given temperatures are $T_1 = 27\,^oC = (27 + 273)\,K = 300\,K$ and $T_2 = 327\,^oC = (327 + 273)\,K = 600\,K$.Substituting these values into the ratio:$\frac{A_2}{A_1} = \left( \frac{600}{300} \right)^4 = (2)^4 = 16$.Thus,the ratio $\frac{A_2}{A_1}$ is $16 : 1$.

The spectrum of a black body at two temperatures $27\,^oC$ and $327\,^oC$ is shown in the figure. Let $A_1$ and $A_2$ be the areas under the two curves respectively. Find the value of $\frac {A_2}{A_1}$.

Similar Questions

$A$ black body at $227^o C$ radiates heat at the rate of $7 \; cal/cm^2 s$. At a temperature of $727^o C$,the rate of heat radiated in the same units will be:

An electric heater kept in a vacuum is heated continuously by passing an electric current. Its temperature:

If the sun's surface radiates heat at $6.3 \times 10^7 \ W m^{-2}$,calculate the temperature of the sun assuming it to be a black body $(\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4})$.

The area of the hole of a heat furnace is $10^{-4} \ m^2$. It radiates $1.58 \times 10^5 \ cal$ of heat per hour. If the emissivity of the furnace is $0.80$,then its temperature is .......... $K$.

$A$ body emits $5 \ W$ of energy at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then the emitted energy becomes .......... $W$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module