Heat & Thermodynamics · JEE Main previous year questions

2015 2 questions

1. Q372015 · 4 Apr 2015 · Shift 1

   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 $p=\frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is:

   1. A.$T\propto \frac{1}{R}$
   2. B.$T\propto \frac{1}{R^3}$
   3. C.$T\propto e^{-R}$
   4. D.$T\propto e^{-3R}$
   Show answer

   Answer: A

2. Q382015 · 4 Apr 2015 · Shift 1

   Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$, where $V$ is the volume of the gas. The value of $q$ is: $\left(\gamma =\frac{C_p}{C_v}\right)$

   1. A.$\frac{\gamma +1}{2}$
   2. B.$\frac{\gamma -1}{2}$
   3. C.$\frac{3\gamma +5}{6}$
   4. D.$\frac{3\gamma -5}{6}$
   Show answer

   Answer: A