How is 'ucs' calculated in pressure of radiation?

AI Thread Summary
The discussion focuses on understanding the calculation of 'ucs' in the context of radiation pressure in Thermal Physics. The equation P = E/c is introduced, where 'u' represents energy density. The user seeks clarification on how 'ucs' is derived as the total energy passing through a surface area per second. Dimensional analysis is suggested as a method to verify the relationship between energy density, speed of light, and area. The user expresses gratitude after gaining clarity on the topic.
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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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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