How is 'ucs' calculated in pressure of radiation?

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SUMMARY

The calculation of 'ucs' in the context of radiation pressure is derived from the relationship P = E/c, where P represents pressure, E is energy, and c is the speed of light. The term 'u' denotes energy density, defined as energy per unit volume. The total energy passing through an area 's' normal to the incident radiation per second is expressed as 'ucs', which can be confirmed through dimensional analysis, showing that u (energy/volume) multiplied by c (length/time) and area (length^2) results in energy/time. This confirms the derivation of the equation.

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  • Understanding of thermal physics concepts, particularly radiation pressure.
  • Familiarity with the equation P = E/c.
  • Knowledge of energy density (u) and its units.
  • Basic skills in dimensional analysis.
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Homework Statement



Revered Members,
While going through pressure of radiation topic in Thermal Physics, i got stumbled at this step.
it has been given P = E/c
If u is the energy density i.e energy per unit volume, then the total energy passing through area 's' of the surface normal to the incident radiation per second = ucs
I don't know how this " ucs " has been arrived.
Please help in this regard. Thanks in advance

Homework Equations





The Attempt at a Solution

 
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Perform a dimensional analysis as follows:

u (energy / volume) = u (energy / length^3)

u (energy / length^3)
c (length / time)
area(length^2) = energy / time

Multiply this out and see if you can match the expected result.
 
Beautiful sir. Thanks a lot, i got it now
 

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