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Mechanical Properties Of Fluids

Question
CBSEENPH11020265

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume straight u equals space straight U over straight V space proportional to space straight T to the power of 4 and pressure.straight p space equals space 1 third open parentheses straight U over straight V close parentheses If the shell now undergoes an adiabatic expansion the relation between T and R is

  • T ∝ e-R

  • T ∝ e-3R

  • T ∝ (1/R)

  • T ∝(1/R3)

Solution

C.

T ∝ (1/R)

According to given equation,
straight p space equals space 1 third open parentheses straight U over straight V close parentheses
rightwards double arrow nRT over straight V space equals space 1 third open parentheses straight U over straight V close parentheses
left square bracket because space pV space equals space nRT right square bracket
or space nRT over straight V space proportional to 1 third straight T to the power of 4
or space VT cubed space equals constant
or space 4 over 3 πR cubed straight T cubed space equals space constant
or space TR space equals constant
straight T proportional to 1 over straight R