Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures ( T _ P ) and ( T _ Q ), respectively, with ( T _ Q

Step-by-step solution

Initially : W ₀= ( T _ P ^4- T _ Q ^4 ) Finally : Putting heat currents equal in steady state : aligned & ( T _ P ^4- T ₁^4 )= ( T ₁^4- T ₂^4 ) & ( T ₁^4- T ₂^4 )= ( T ₂^4- T _ Q ^4 ) aligned Adding : T _ P ^4- T ₁^4= T ₂^4- T _ Q ^4 T ₁^4+ T ₂^4= T _ P ^4+ T _ Q ^4 and T ₁^4- T ₂^4= T _ P ^4- T ₁^4 Adding : T ₁^4= 2 ~T _ P ^4+ T _ Q ^4 3 So W _ S = ( T _ P ^4- T ₁^4 )= ( T _ P ^4- ( 2 ~T _ P ^4+ T _ Q ^4 3 ) )= ( T _ P ^4- T _ Q ^4 3 ) hence W _ S W ₀ =3