3. Given that the internal energy U of blackbody radiation in a cavityof volume V at temperature T is given by U = aVT, where a isindependent of both V and T, show by thermodynamic reasoning thatthe free energy, F, and the entropy, S, of the radiation must have theforms:-jaVT* + Tf(V)F =s = aVT° - {(V)4where f(V) is an unknown function of V. Assuming S vanishes atT = 0 (because there is no radiation) or assuming the third law ofthermodynamics:as(),asT + 0avshow that the radiation pressure is given by1 UP =3 V

Radiation pressure is defined as one third of the energy density per unit volume. Radiation pressure…

Given that the internal energy U of blackbody radiation in a cavity of volume V at temperature T is given by U = aVT*, where a is independent of both V and T, show by thermodynamic reasoning that the free energy, F, and the entropy, S, of the radiation must have the forms: 1 P = --aVT* +Tf(V) » 4 S = ; aVT - f(V) , | where f(V) is an unknown function of V. Assuming S vanishes at T = 0 (because there is no radiation) or assuming the third law of thermodynamics: as as T +0 av T show that the radiation pressure is given by 1 U P = 3 V

Given that the internal energy U of blackbody radiation in a cavity of volume V at temperature T is given by U = aVT, where a is independent of both V and T, show by thermodynamic reasoning that the free energy, F, and the entropy, S, of the radiation must have the forms: 1 P = --aVT +Tf(V) » 4 S = ; aVT - f(V) , | where f(V) is an unknown function of V. Assuming S vanishes at T = 0 (because there is no radiation) or assuming the third law of thermodynamics: as as T +0 av T show that the radiation pressure is given by 1 U P = 3 V

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Wien's displacement law

Students often get confused between Wien's displacement law and Planck's radiation law. Although both are historically related, yet they are conceptually different. Planck's law helps determine the spectrum of a blackbody, while Wien's law determines the relationship between peak wavelength and temperature.

Question

100%

3. Given that the internal energy U of blackbody radiation in a cavity
of volume V at temperature T is given by U = aVT, where a is
independent of both V and T, show by thermodynamic reasoning that
the free energy, F, and the entropy, S, of the radiation must have the
forms:
-jaVT* + Tf(V)
F =
s = aVT° - {(V)
4
where f(V) is an unknown function of V. Assuming S vanishes at
T = 0 (because there is no radiation) or assuming the third law of
thermodynamics:
as
(),
as
T + 0
av
show that the radiation pressure is given by
1 U
P =
3 V

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