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Test: Thermo And Statistical - 2 - Physics MCQ


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20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Thermo And Statistical - 2

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Test: Thermo And Statistical - 2 - Question 1

If light was of purely wave nature, the total energy radiated by a black-body would be (T is the temperature of the blackbody)

Detailed Solution for Test: Thermo And Statistical - 2 - Question 1

If light was of purely wave nature, then electromagnetic wave theory predicts that the total energy radiated by a black body over all wavelength is infinite. This is known as ultraviolet catastrophe.

Test: Thermo And Statistical - 2 - Question 2

Two particles are said to be distinguishable when

Detailed Solution for Test: Thermo And Statistical - 2 - Question 2

In Quantum mechanical description of particles, the de-Broglie wavelength of a particles is a measure of the wave character of the particle and hence, in a way, measures the inherent imprecision in locating a particle. It means that a particle is speed over a length and not localized at precisely fixed spot. Hence, the average distance between two particles (mean free path) should be large as compared to their de-Broglie wavelength for them to be ‘distinguishable’.
Options (a) and (d) are properties that are associated with ‘indistingunishable’ particles.

Test: Thermo And Statistical - 2 - Question 3

A reversible heat engine (Carnot engine) with a monatomic gas molecules as the working substance. If a diatomic molecules is used as the working substance, the efficiency of the same engine is

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The efficiency of a Cannot engine does not depend on the working substance.

*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 4

Due to outside heat and green house effect in a glass-sealed room in a building, the energy inside increases at the rate of 0.5 kJ hour (which leads to increase in the temperature of the room). To make the room comfortable. an air conditioner is fitted. The room is to be kept at a cozy 200C against 400C outside. Assuming the air-conditioner is able to work at its maximum performance. How many units of electricity is consumed by the air-conditioner (in units of kJ hour)? (upto 2 decimal places)


Detailed Solution for Test: Thermo And Statistical - 2 - Question 4


Test: Thermo And Statistical - 2 - Question 5

The plot that describes an engine underdoing a thermodynamic process with maximum efficiency is 

Detailed Solution for Test: Thermo And Statistical - 2 - Question 5

A Cannot engine lias the m axim um efficiency. In the cyclic process of a cannot engine, two path s are isothermals and the other two are adiabatics (or isentropics).

Test: Thermo And Statistical - 2 - Question 6

The density fluctuations in a pure substance are maximum at its 

Detailed Solution for Test: Thermo And Statistical - 2 - Question 6

The number density fluctuations in a grand canonical ensemble is given by

Now, at the critical point of a substance, the isothermal compresibility  becomes large (maximum). 
As a result, number density fluctuations are Large at critical point.
Hence mass density fluctuations are also large (or maximum) at the critical point.

Test: Thermo And Statistical - 2 - Question 7

The density of states for a system of 4 electrons in a 2-D space having total energy in the range (E, E + dE) is proportional to

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The number of allowed microstates for N particles are

Test: Thermo And Statistical - 2 - Question 8

A collection of 20 non-rigid diatomic molecules can be described by a phase space of dimension ________


Detailed Solution for Test: Thermo And Statistical - 2 - Question 8

Degree of freedom of one non rigid diatomic molecule

Test: Thermo And Statistical - 2 - Question 9

A particle of mass m starts from rest a height H and moves under the gravitational force mg. It strikes a horizontal surface with a coefficient of restitution equal to a perfect one. The phase space diagram of the particle is ('h' is height from the surface)

Detailed Solution for Test: Thermo And Statistical - 2 - Question 9




*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 10

3 identical spin 1/2 fermions are to be filled in 2 non-degenerate energy states. If a magnetic field is switched on in the direction, how many distinct configurations of fermions in the given energy states arise?


Detailed Solution for Test: Thermo And Statistical - 2 - Question 10

3 identical fermions are filled in 2 non degenerate energy states.
 These 2 states are possible.
But in presence of a magnetic field, there arises two configuration of each of the above two splits in presence Df magnetic field. Therefore 4 distinct configurations arise for the given system.

*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 11

A rigid linear diatomic ideal gas at room temperatrue is expanded at constant presure. What percentage of the heat supplied is used to increase the internal energy of the gas? (Answer must be given upto 2 decimal places)


Detailed Solution for Test: Thermo And Statistical - 2 - Question 11

For Linear diatomic molecule (ligid).

Test: Thermo And Statistical - 2 - Question 12

A classical ideal gas of atoms with masses 'm' is confined in a 2-D potential given by

at a temperature T. If kis the Boltzmann constant, the value of 

Detailed Solution for Test: Thermo And Statistical - 2 - Question 12


*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 13

If a body radiates heat to the outside such that the entropy of the universe increases propotional to T2. and the heat radiated is propotional to Tα, then α is __________


Detailed Solution for Test: Thermo And Statistical - 2 - Question 13

If entropy increases as T2, we have 

Test: Thermo And Statistical - 2 - Question 14

What is the minimum attainable pressure of an ideal gas in the process by T= a+bV2?

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*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 15

In S-dimensions, two metals A and B have the ratio of Fermi energies as  If the ratio of the number densities of free electrons in the metals is 4 : 9, then the value of S' is _______


Detailed Solution for Test: Thermo And Statistical - 2 - Question 15

In S-dimensions. the particle density varies with Fermi energy as

Test: Thermo And Statistical - 2 - Question 16

A vertically suspended square plate of side 'a' acts as adsorbent molecules of particular gas having N identical molecules out of a mixture once adsorbed, the gas molecules are free to move in the square plate but do not possess the energy to escape. The average energy of the gas at low temperatures (mga » kBT) is

Detailed Solution for Test: Thermo And Statistical - 2 - Question 16




*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 17

3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB = ________  kB (upto 2 decimal places)


Detailed Solution for Test: Thermo And Statistical - 2 - Question 17

If the particles are distinguishable, then 

If the integral spin particles are indistinguishable, then

*Answer can only contain numeric values
Test: Thermo And Statistical - 2 - Question 18

3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB' be the entropy if they are indistinguishable particles of integral spin. Then SD-SB = _____ kB (upto 2 decimal places)


Detailed Solution for Test: Thermo And Statistical - 2 - Question 18

The single particle partition function is 

Test: Thermo And Statistical - 2 - Question 19

Photons can undergo Bose-Einstein condensation because

Detailed Solution for Test: Thermo And Statistical - 2 - Question 19

Photon can undergo Bose-Einstein condensation due to the following properties 
(i) They have symmetric wavefiuictions with respect to particle exchange
(if) They can have overlapping wavefiuictions.
(iii) The chemical potential of photons is zero.

Test: Thermo And Statistical - 2 - Question 20

N non-interacting particles with magnetic moments are subjected to a magnetic field along the  direction. Each magnetic moment lias a doubly degenerate energy level zero and non-degenerate energy levels of energies -μH and μH. The collection is in thermal equilibrium with a heat reservoir at temperature T. The magnetisation per particle is

Detailed Solution for Test: Thermo And Statistical - 2 - Question 20


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