How to Calculate Radiation Pressure Inside a Kiln?

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SUMMARY

The discussion focuses on calculating radiation pressure inside a kiln with a volume of 1 m³ and a temperature of 1500 K. The total energy was calculated using the formula U/V = 8π⁵(kT)⁴/15(hc)³, resulting in U = 3.83 kJ. To find radiation pressure, participants confirmed that it is derived from energy density rather than total energy, emphasizing the importance of using the relation p = -∂F/∂V, where F is the free energy. The conversation also highlighted the need for understanding entropy and its relation to pressure calculations.

PREREQUISITES
  • Understanding of electromagnetic radiation principles
  • Familiarity with thermodynamic equations, specifically PV = NkT
  • Knowledge of energy density calculations
  • Basic concepts of free energy and entropy
NEXT STEPS
  • Study the derivation of radiation pressure from energy density
  • Learn about the relationship between entropy and free energy in thermodynamics
  • Explore the implications of temperature on radiation pressure calculations
  • Investigate the comparison of radiation pressure with air pressure in various conditions
USEFUL FOR

Students in physics or engineering, researchers in thermodynamics, and professionals working with high-temperature processes in kilns or similar environments.

S_Flaherty
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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?
 
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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}.
 
clamtrox said:
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
 

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