A black rectangular surface of area A emits e | 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 energy emitted per unit time (power) $P$ by a black body is given by $P = \sigma A T^4$, where $\sigma$

Vedclass · Accepted Answer

$E$

Vedclass · Answer

(A) According to the Stefan-Boltzmann law, the energy emitted per unit time (power) $P$ by a black body is given by $P = \sigma A T^4$, where $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area, and $T$ is the absolute temperature in Kelvin.Initial state: $P_1 = E = \sigma A T_1^4$, where $T_1 = 27 + 273 = 300 	ext{ K}$.Final state: The length and breadth are reduced to $1/4$ of their initial values, so the new area $A' = (A/4) 	imes (1/4) = A/16$. The new temperature $T_2 = 327 + 273 = 600 	ext{ K}$.The new power $P_2 = \sigma A' T_2^4 = \sigma (A/16) (600)^4$.Taking the ratio: $P_2 / P_1 = [\sigma (A/16) (600)^4] / [\sigma A (300)^4] = (1/16) 	imes (600/300)^4 = (1/16) 	imes 2^4 = 16/16 = 1$.Therefore, $P_2 = E$.

$A$ black rectangular surface of area $A$ emits energy $E$ per unit time at $27^{\circ}C$. If length and breadth are reduced to $(1/4)^{th}$ of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per unit time becomes:

Similar Questions

If the radius of a star is $R$ and it acts as a black body,what would be the temperature of the star,in which the rate of energy production is $Q$? ($\sigma$ stands for Stefan's constant)

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat is:

The outer surface of a star in the form of a sphere radiates heat as a black body at temperature $T$. The total radiant energy per unit area,normal to the direction of incidence,received at a distance $R$ from the center of a star of radius $r$ is $(R > r)$ ($\sigma =$ Stefan's constant).

If the temperature of a perfectly black body is increased by $50\%$,find the percentage increase in the amount of radiation emitted from its surface.

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

Vedclass Test Series

Exam Paper Generator

Online Exam Module