QJEEM15Phc97e: JEE Main 2015 Physics - Class 11 JEEM15Phc97e Solution: Consider a spherical shell of radius R at temperature T . The…

Question

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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 = \frac{U}{V} \propto T^{4}

and pressure

p = \frac{1}{3} (\frac{U}{V})

. If the shell now undergoes an adiabatic expansion the relation between

T

and

R

is:

Accepted Answer

As,

P = \frac{1}{3} (\frac{U}{V})

But

\frac{U}{V} = K T^{4}

So,

P = \frac{1}{3} K T^{4}

or

\frac{u R T}{V} = \frac{1}{3} K T^{4}

[

As

P V = u R T

]

\frac{4}{3} π R^{3} T^{3} =

c o n s t a n t

∴

T \propto \frac{1}{R}

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