GATE PH topic:thermodynamics-statistical-physics PYQs & Answers — Page 6

Questions 51–60 of 60. Imported answers require independent review unless marked reviewed.

Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated from A to that from B is ______.

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The partition function of an ensemble at a temperature

where

is the Boltzmann constant. The heat capacity of this ensemble at

, where the value of X is ______ (up to one decimal place).

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The quantum effects in an ideal gas become important below a certain temperature

when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass

kg and number density

(up to one decimal place).\n\n(

)

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Consider a triatomic molecule of the shape shown in the figure below in three dimensions. The heat capacity of the molecule at high temperature (temperature much higher than the vibrational and rotational energy scales of the molecule but lower than its bond dissociation energies) is:

Your answerChoose one option.

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A reversible Carnot engine is operated between temperatures

and

(

) with a photon gas as the working substance. The efficiency of the engine is

Your answerChoose one option.

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Water freezes at

at atmospheric pressure (

). The densities of water and ice at this temperature and pressure are 1000 kg/m

and 934 kg/m

respectively. The latent heat of fusion is

, the pressure required for depressing the melting temperature of ice by

is ______ GPa. (up to two decimal places)

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Consider

non-interacting, distinguishable particles in a two-level system at temperature

. The energies of the levels are 0 and

, where

. In the high temperature limit (

), what is the population of particles in the level with energy

Your answerChoose one option.

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The integral

is equal to ________. (up to two decimal places).

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The energy density and pressure of a photon gas are given by

and

, where

is the temperature and

is the radiation constant. The entropy per unit volume is given by

. The value of

is ________. (up to two decimal places).

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Consider two particles and two non-degenerate quantum levels 1 and 2. Level 1 always contains a particle. Hence, what is the probability that level 2 also contains a particle for each of the two cases: (i) when the two particles are distinguishable and (ii) when the two particles are bosons?

Your answerChoose one option.

(i) 1/2 and (ii) 1/3

(i) 1/2 and (ii) 1/2

(i) 2/3 and (ii) 1/2

(i) 1 and (ii) 0

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GATE PH topic:thermodynamics-statistical-physics PYQs

Question 52

Question 53

Question 55

Question 9

Question 24

Question 29

Question 33

Question 38

Question 43

Question 49