InterviewSolution
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InterviewSolution
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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))` |
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Answer» Correct Answer - C Here, `P= 1/3(U/V) and u=U/V propT^(4)` or `u=U/V=KT^(4)` `:.P=1/3KT^(4), As PV=nRT, :. P=(nRT)/V` or `(nRT)/V= KT^(4) or (nR)/V=KT^(3)` `:. V prop T^(-3) or VT^(3)= constant` As volume, `V= 4/3 piR^(3) :. 4/3piR^(3)T^(3)=constant` or `R^(3)T^(3)= constant` `RT= constant or T prop 1/R` |
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