GATE PH topic:thermodynamics-statistical-physics PYQs & Answers — Page 5

Questions 41–50 of 60. Imported answers require independent review unless marked reviewed.

For a gas of non-interacting particles, the probability that a particle has speed

in the interval

is given by

is the energy of a particle, then the maximum in the corresponding energy distribution in units of

occurs at _____ (rounded off to one decimal place).

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The Planck’s energy density distribution is given by

. At long wavelengths, the energy density of photons in thermal equilibrium with a cavity at temperature

varies as

, where

is _____.

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Consider a one-dimensional gas of

non-interacting particles of mass

with the Hamiltonian for a single particle given by,

The high temperature specific heat in units of

(

is the Boltzmann constant) is

Your answerChoose one option.

1.5

2.5

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A large number

of ideal bosons, each of mass

, are trapped in a three-dimensional potential

. The bosonic system is kept at temperature

which is much lower than the Bose-Einstein condensation temperature

. The chemical potential (

) satisfies

Your answerChoose one option.

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At temperature

Kelvin (K), the value of the Fermi function at an energy 0.5 eV above the Fermi energy is 0.01. Then,

, to the nearest integer, is

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In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K. Neglecting the specific heat of the container, the change in the entropy of the system in J/K on attaining thermal equilibrium (rounded off to two decimal places) is (Specific heat of water is 4.2 kJ/kg-K and the latent heat of ice is 335 kJ/kg).

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Consider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the system B has energy 2 units, the entropy of the combined system is

. The value of

is ______

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Three particles are to be distributed in four non-degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons, respectively, is

Your answerChoose one option.

(i) 24, (ii) 4

(i) 24, (ii) 20

(i) 64, (ii) 20

(i) 64, (ii) 16

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A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy

state. Both states are non-degenerate. If the total energy of this ensemble is

, its entropy will be ______

(up to one decimal place), where

is the Boltzmann constant.

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An air-conditioner maintains the room temperature at 27 °C while the outside temperature is 47 °C. The heat conducted through the walls of the room from outside to inside due to temperature difference is 700 W. The minimum work done by the compressor of the air-conditioner per unit time is ______ W.

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GATE PH topic:thermodynamics-statistical-physics PYQs

Question 54

Question 55

Question 5

Question 7

Question 23

Question 49

Question 51

Question 33

Question 49

Question 51