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GATE-2021 (52) The dimension of radiant emittance (Expected solution)

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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

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