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=VU∝T4 and pressure p=31(VU). If the shell now undergoes an adiabatic expansion, the relation between T and R is(a) T∝e−R(b) T∝e−3R(c) T∝R1(d) T∝R31

Exp. (c)According to question,p=31(VU)⇒VnRT=31(VU)[∵pV=nRT]or VnRT∝31T4 or VT3= constantor 34πR3T3= constant or TR= constant⇒T∝R1

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Consider a spherical shell of radius R at temperature T. The b

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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
(a) $T \propto e^{- R}$
(b) $T \propto e^{- 3 R}$
(c) $T \propto \frac{1}{R}$
(d) $T \propto \frac{1}{R ^{3}}$

Views: 5,522 students

Updated on: Mar 30, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2015

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Chloe Discussed

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
(a)

T \propto e^{- R}

(b)

T \propto e^{- 3 R}

(c)

T \propto \frac{1}{R}

(d)

T \propto \frac{1}{R ^{3}}

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Exp. (c)
According to question,

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

\Rightarrow \frac{n RT}{V} = \frac{1}{3} (\frac{U}{V}) [∵ p V = n RT]

\frac{n RT}{V} \propto \frac{1}{3} T^{4}

V T^{3} =

constant
or

\frac{4}{3} π R^{3} T^{3} =

constant or

TR =

constant

\Rightarrow T \propto \frac{1}{R}

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Question Text	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 (a) $T \propto e^{- R}$ (b) $T \propto e^{- 3 R}$ (c) $T \propto \frac{1}{R}$ (d) $T \propto \frac{1}{R ^{3}}$
Updated On	Mar 30, 2023
Topic	Thermodynamics
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	350
Avg. Video Duration	9 min

Text solutionVerified

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