The SI unit and dimension of Stefan's constan | vedclass

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

Question

(D) According to Stefan's law,the energy emitted by a body per unit area per unit time is proportional to the fourth power of its absolute temperature

Vedclass · Accepted Answer

$\frac{J}{m^2 s K^4}, [M^1 L^0 T^{-3} K^{-4}]$

Vedclass · Answer

(D) According to Stefan's law,the energy emitted by a body per unit area per unit time is proportional to the fourth power of its absolute temperature.$E = \sigma T^4$Where $E$ is the energy emitted per unit area per unit time,$T$ is the absolute temperature in Kelvin,and $\sigma$ is Stefan's constant.Rearranging for $\sigma$: $\sigma = \frac{E}{T^4}$.The unit of $E$ is $\frac{J}{m^2 s}$.Therefore,the unit of $\sigma$ is $\frac{J}{m^2 s K^4}$.The dimensions of energy are $[M L^2 T^{-2}]$,area is $[L^2]$,time is $[T]$,and temperature is $[K]$.$\sigma = \frac{[M L^2 T^{-2}]}{[L^2] [T] [K^4]} = [M^1 L^0 T^{-3} K^{-4}]$.

The $SI$ unit and dimension of Stefan's constant $\sigma$ in the case of Stefan's law of radiation are

Similar Questions

$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made half and the temperature is made $4T$,the rate of radiation will be: (in $E$)

Compare the rate of loss of heat from a metal sphere at $627^{\circ} C$ with the rate of loss of heat from the same sphere at $327^{\circ} C$,if the temperature of the surrounding is $27^{\circ} C$. (nearly)

$A$ black body radiates energy at the rate of $E \ W/m^2$ at a high temperature $T \ K$. When the temperature is reduced to $\frac{T}{2} \ K$,the radiant energy will be

$A$ black rectangular surface of area '$A$' emits energy '$E$' per second at $27^{\circ} C$. If length and breadth are reduced to $\frac{1}{3}$ of their initial values and the temperature is raised to $327^{\circ} C$,then the energy emitted per second becomes:

Vedclass Test Series

Exam Paper Generator

Online Exam Module