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5.%20Thermodynamics and Statistical Physics NET-JRF%20June%202011-Dec%202014

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics

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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES THERMODYNAMICS AND STATISTICAL PHYSICS NET/JRF (JUNE-2011) Q1. Consider the transition of liquid water to steam as water boils at a temperature of 100oC under a pressure of 1 atmosphere. Which one of the following quantities does not change discontinuously at the transition? (a) The Gibbs free energy (c) The entropy Ans: (b) The internal energy (d) The specific volume (a) Solution: In first order transition Gibbs free energy is continuous. Q2. A particle is confined to the region x 0 by a potential which increases linearly as u x u 0 x . The mean position of the particle at temperature T is (a) Ans: k BT u0 (b) k BT / u0 2 k BT u0 (c) (d) u 0 k B T (a) p2 u x 0 1 2mkBT Solution: Partition function Z e dp e kBT dx and x xp x dxdpx h x xe e Q3. p2 2 mk BT dp e 2 p 2 mk BT dp e u0 x k BT u0x k BT dx xe 0 e dx 0 0 x k BT x 0 k BT dx dx k BT u 2 0 k BT u 0 te t dt 0 e t dt k BT u0 0 A cavity contains blackbody radiation in equilibrium at temperature T. The specific heat per unit volume of the photon gas in the cavity is of the form CV T 3 , where is a constant. The cavity is expanded to twice its original volume and then allowed to equilibrate at the same temperature T. The new internal energy per unit volume is (a) 4 T 4 Ans: (b) 2 T 4 (c) T 4 (d) T 4 4 (d) Solution: du Cv dT T dT u 3 T 4 4 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1

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