JEE Main 2015 · 4 Apr · Shift 1 · Physics Q9

← JEE Main 2015 · 4 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 9 of 90

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 $u=\dfrac UV\propto T^4$ and pressure $p=\dfrac13\left(\dfrac UV\right)$ . If the shell now undergoes an adiabatic expansion the relation between T and R is :

T\propto e^{-R}

T\propto e^{-3R}

T\propto\dfrac1R

T\propto\dfrac1{R^3}

Answer and worked solution

Official answer: C

For the photon gas, $p=\frac u3$ and $u\propto T^4$ . In an adiabatic process $dU=-p\,dV$ with $U=uV$ :
$d(uV)=-\frac u3dV\implies V\,du=-\frac43u\,dV\implies u\propto V^{-4/3}.$
So $T^4\propto V^{-4/3}$ , $T\propto V^{-1/3}\propto\dfrac1R$ .

Topics:Thermodynamic processes Radiation and Stefan's law

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JEE Main 2015 · 4 Apr · Shift 1, Physics question 9