Basic Maths and Units and DimensionsHard

Question

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 u = U/V ∝ T4 and pressure p = . If the shell now undergoes an adiabatic expansion the relation between T and R is -

Options

A.T ∝ 1 / R
B.T ∝ 1 / R3
C.T ∝ e-R
D.T ∝ e-3R

Solution

P =
P ∝ T4
using PV = nRT
∝ T3
⇒ T ∝

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