Two bodies A and B of equal surface area have | vedclass

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

Question

(D) According to Stefan-Boltzmann law, the power radiated is $P = e A \sigma T^4$. Since the bodies have equal surface area and radiate at the same ra

Vedclass · Accepted Answer

$\frac{3}{2} \mu m$

Vedclass · Answer

(D) According to Stefan-Boltzmann law, the power radiated is $P = e A \sigma T^4$. Since the bodies have equal surface area and radiate at the same rate $(P_A = P_B)$, we have $e_A T_A^4 = e_B T_B^4$.Given $e_A = 0.01$, $e_B = 0.81$, and $T_A = 5802 \ K$.Substituting the values: $0.01 	imes (5802)^4 = 0.81 	imes T_B^4$.Taking the fourth root on both sides: $T_B = T_A 	imes (0.01 / 0.81)^{1/4} = 5802 	imes (1/81)^{1/4} = 5802 / 3 = 1934 \ K$.From Wien's displacement law, $\lambda_A T_A = \lambda_B T_B = b$ (where $b \approx 2898 \ \mu m \cdot K$).Thus, $\lambda_A = b / T_A = 2898 / 5802 \approx 0.5 \ \mu m$.Given $\lambda_B - \lambda_A = 1 \ \mu m$, so $\lambda_B = 1 + 0.5 = 1.5 \ \mu m = \frac{3}{2} \ \mu m$.

Similar Questions

$A$ body at $1500 \ K$ emits maximum energy at a wavelength $20,000 \ \mathring{A}$. If the Sun emits maximum energy at a wavelength $5500 \ \mathring{A}$,then the temperature of the Sun is ....... $K$.

If the wavelengths of maximum intensity of radiation emitted by the Sun and the Moon are $0.5 \times 10^{-6} \, m$ and $10^{-4} \, m$ respectively,then the ratio of their temperatures is ............

$A$ black body emits radiation of maximum intensity at wavelength $\lambda$ at temperature $T \ K$. Its corresponding wavelength at temperature $1.5 \ T \ K$ will be

If a black wire of platinum is heated, its colour first appears red, then yellow, and finally white. This can be understood on the basis of:

The law used in the measurement of the temperature of stars is .........

Vedclass Test Series

Exam Paper Generator

Online Exam Module