GATE-2018 (24) :Wyllie – Time average equation

52. The dimension of radiant emittance of a blackbody as per Stefan-Boltzmann law is:

1) M¹ L² T^-2

2) M⁰ L¹ T^-1

3) M¹ L⁰ T^-3

4) M¹ L^-1 T^-2

 Solution:

Black body radiant emittance $E=\sigma T^4$

$\sigma$ - Stefan Boltzmann constant =$5.67037*10^{-8} W/m^2K^4$

T- Thermodynamic Temperature

$E= \frac{W}{m^2K^4} K^{4}$

 $E=\frac{W}{m^2}$

 1watt=joule/second

 $E=\frac{joule}{s.m^2}$ ---(1)

 Joule is the unit of work

 work= Force* displacement

       =N.m

       =$\frac{Kg.m^2}{s^2 }$    

 Substitute in above equation,

  $E=\frac{joule}{s.m^2}$

  $E=\frac{kg.m^2}{s^3.m^2}$

  $E=\frac{kg}{s^3}$

 

  Units of Emittance E is $M^1 L^0 T^-3$