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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 alpha (1)/(R)`

B

`T alpha (1)/(R^(3))`

C

` T alpha e^(-R)`

D

`T alpha e^(-3R)`

Text Solution

Verified by Experts

The correct Answer is:
A
`P= (1)/(3)((U)/(V))`
`P alpha T^(4) "using" PV = nRT`
`(1)/(V) alpha T^(3)`
`implies T alpha(1)/(R)`
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