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Consider a spherical shell of radius R a...

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 propT^4` and pressure `P=1/3(U/V)`. If the shell now undergoes an adiabatic expansion the relation between T and R is :

A

`T prop e^(-R)`

B

`T prop e^(-3R)`

C

`T prop 1/R`

D

`T prop 1/R^3`

Text Solution

Verified by Experts

The correct Answer is:
C
As `P=1/3(U/V) and U/V = KT^4`
`:. P=1/3 KT^(4)`
`implies (nRT)/V=1/2 KT^4 ` [ as PV = nRT]
`implies VT^3` = constant
`implies 4/3 pi R^3 T^3` = constant `implies T prop 1/R`
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