How to Calculate Radiation Pressure Inside a Kiln?

[S_Flaherty]

Homework Statement

Consider the electromagnetic radiation inside a kiln, with a volume of 1 m³ and a temperature of 1500 K.

Calculate the radiation pressure inside the kiln. How does it compare with the air pressure?

Homework Equations

PV = NkT

The Attempt at a Solution

I got the total energy using U/V = 8π⁵(kT)⁴/15(hc)³ and got U = 3.83 kJ. To find the radiation pressure would I just divide the energy by c? Also, how do I find the air pressure if I don't have a value for N?

 

[clamtrox]

Radiation pressure is related to the energy density, not total energy. If you don't have a formula at hand, you can calculate the relation pretty easily by using for instance $$C_v = \frac{\partial U}{\partial T} = T\frac{\partial S}{\partial T}$$ to find entropy. Use that to find the free energy $F = U - TS$ and pressure $p = -\frac{\partial F}{\partial V}$.

 

[S_Flaherty]

Radiation pressure is related to the energy density, not total energy. If you don't have a formula at hand, you can calculate the relation pretty easily by using for instance $$C_v = \frac{\partial U}{\partial T} = T\frac{\partial S}{\partial T}$$ to find entropy. Use that to find the free energy $F = U - TS$ and pressure $p = -\frac{\partial F}{\partial V}$.

Thanks!, this helps a lot