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

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter8: Quantum Mechanics In Three Dimensions

Section: Chapter Questions

Problem 15P

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