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Consider a spherical shell of radius R at temperature T. The black body radiation in side it can be considered as an ideal gas of photons with internal energy per unit volume u=fraction numerator sigma over denominator V end fraction proportional to T to the power of 4 end exponentand pressure p equals fraction numerator 1 over denominator 3 end fraction open parentheses fraction numerator U over denominator V end fraction close parentheses If the shell now undergoes an adiabatic expansion the relation between T and R is:

  1. T proportional to fraction numerator 1 over denominator R end fraction    
  2. T proportional to fraction numerator 1 over denominator R to the power of 3 end exponent end fraction    
  3. T proportional to e to the power of negative R end exponent    
  4. T proportional to e to the power of negative 3 R end exponent    

The correct answer is: T proportional to fraction numerator 1 over denominator R end fraction

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