Thermal and Statistical Physics - Quanta: BS/MSc Physics Books

1: What survives the averaging in the measurements of an observable?

a. Some combinations of independent observables

b. Some combinations of dependent observables

c. Some combinations of Time dependent quantities

d. None of these

2: A system is in thermodynamic equilibrium if it satisfies the stringent requirements of

a. Mechanical Equilibrium

b. Thermal Equilibrium

c. Chemical Equilibrium

d. All of these.

3: For a simple enclosed in adiabatic walls, the only permissible form of energy transfer is

a. Heat

b. Phonons

c. Photons

d. work

4: Entropy ‘S’ vanishes if

a. $\left|\frac{\partial S}{\partial U}\right|V,N=0$

b. $\left|\frac{\partial U}{\partial S}\right|V,N=0$

c. $\ \left|\frac{\partial U}{\partial S}\right|V,N=\frac{1}{T}$

d. $\mathbf{\left|\frac{\partial S}{\partial U}\right|V,N=\frac{1}{T}}$

5: The coefficient of thermal expansion (expansivity) β is defined as

a. $\beta=\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)$

b. $\beta=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)$

c. $\beta=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)$

d. $\mathbf{\beta=-\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)}$

6: C_p-C_v is equal to

a. $T\left(\frac{\partial S}{\partial P}\right)\left(\frac{\partial V}{\partial P}\right)$

b. $T\left(\frac{\partial S}{\partial P}\right)\left(\frac{\partial V}{\partial T}\right)$

c. $\mathbf{\frac{TV\beta^2}{K_T}}$

d. $\frac{TV\beta^2}{C_V}$

7: The equation $\mathbf{\left(\frac{\partial U}{\partial V}\right)=T\left(\frac{\partial P}{\partial T}\right)-P}$ is known as

a. Heat-capacity equation

b. TdS equation

c. Energy equation

d. None

8: The Maxwell relation is given by

a. $\left(\frac{\partial S}{\partial P}\right)=-\left(\frac{\partial V}{\partial T}\right)$

b. $\left(\frac{\partial V}{\partial S}\right)=-\left(\frac{\partial T}{\partial P}\right)$

c. $\mathbf{\left(\frac{\partial P}{\partial S}\right)=-\left(\frac{\partial T}{\partial V}\right)}$

d. $\left(\frac{\partial S}{\partial V}\right)=-(\frac{\partial P}{\partial T})$

9: Which one of the following is not a thermodynamic potential

a. Entropy

b. Enthalpy

c. Internal energy

d. Volume

10: Sublimation is an example of phase transition known as

a. Lambda transition

b. First-order transition

c. Second-order transition

d. Higher-order transition

11: The equilibrium state (macro-state) of a system corresponds to state of

a. Maximum probability

b. Minimum probability

c. Ordered state

d. All of above

12: The particles obeying Fermi-Dirac statistics have spin

a. Integral

b. Half integral

c. Zero

d. None of above

13: The particles which are identical, indistinguishable and have integral spin are called

a. Bosons

b. Fermions

c. Phonons

d. All of above

14: The dimensions of phase space volume are

a. (length x momentum)³

b. (work x time)³

c. (angular momentum)³

d. (length)³

15: Statistical methods give greater accuracy when number of observations is

a. Very small

b. Very large

c. Neither very small nor very large

d. None of above

16: The macro-states which are allowed under a constraint are called ……macro-states

a. Particular

b. Inaccessible

c. Accessible

d. None of above

17: In Maxwell-Boltzmann statistics , particles are treated as

a. Distinguishable

b. Indistinguishable

c. Photons

d. All of above

18: Free electrons in metals obey ………statistics

a. Maxwell-Boltzmann

b. Classical

c. Fermi-Dirac

d. Bose-Einstein

19: Minimum size of a cell in quantum statistics is

a. h³

b. $\hbar^3$

c. Zero

d. None of above

20: Molecules of N₂at S.T.P. obey ………statistics

a. Maxwell-Boltzmann

b. Classical

c. Fermi-Dirac

d. Bose-Einstein

21: The value of γ for a gas is 1.66, then gas is

a. O₂

b. H₂

c. Ne

d. N₂

22: The dimensions of universal gas constant R is

a. M²L²T^-2

b. ML²T^-2

c. MLT^-2

d. M²L²T^-2

23: The temperature which is same in and is

a. -40

b. 40

c. -20

d. 20

24: At what temperature do the Fahrenheit and kelvin scales coincide?

a. 273

b. -100

c. 574

d. 844

25: Absolute temperature can be calculated by

a. Mean square speed

b. Motion of molecules

c. a and b

d. Amplitude

26: When the temperature difference between the source and sink increases, the efficiency of heat engine will

a. Decrease

b. Increase

c. is not affected

d. None of them

27: The thermodynamic temperature scale was given by

a. Kelvin

b. Fahrenheit

c. Dewar

d. Carnot

28: A Carnot engine can be 100% efficient if LTR is at

a. 0C

b. 0K

c. 0F

d. 273K

29: A piece of ice at 0 is dropped into water at 0 the ice will

a. Melt

b. Partially melts

c. Not melts

d. Be converted to water

30: In free expansion of gas the internal energy of system

a. Decreases

b. is unchanged

c. Changes

d. Increases

31: A random variable x has a set of possible outcomes, which may be

a. Discrete

b. Continuous

c. Both

d. None of these

32: The probability is always

a. Zero

b. Positive

c. Negative

d. None of these

33: The Normalization of probability requires that

a. P(S)=0

b. P(S)=1

c. P(S)=+∞

d. P(S)=-∞

34: Objective probabilities are obtained through

a. Experiments

b. Theories

c. Both a and b

d. None of these

35: The cumulants are the generator of

a. PDF

b. CPF

c. Mean

d. Moments

36: The characteristic function is the generator of

a. PDF

b. CPF

c. Mean

d. Moments

37: The expectation values for powers of a random variable are known as

a. PDF

b. CPF

c. Mean

d. Moments

38: The Mean value for Gaussian distribution is given by

a. <x>=λ

b. <x>=NP’_A

c. <x>=aT

d. None of these

39: The Mean value for a Poisson distribution is given by

a. <x>=λ

b. <x>=NP’_A

c. <x>=aT

d. None of these

40: The Poisson distribution can be taken as

a. The generalization of Binomial distribution

b. The generalization of Gaussian distribution

c. The limit to the Binomial distribution

d. The limit to the Gaussian distribution

41: Particles which obey Pauli-Exclusion Principle are termed as

a. Maxwellians

b. Bosons

c. Fermions

d. None of these

42: At least, how many macroscopic observables are required to specify the state of a system

a. One

b. Two

c. Three

d. Four

43: A state where all the parameters of the constituent particles are specified is called

a. Excited state

b. Microstate

c. Macrostate

d. Both b and c

44: The statistical weight represents the number of

a. Excited state

b. Microstate

c. Macrostate

d. Both b and c

45: To find a Microstate which contains a large number of microstates, represents thermodynamic equilibrium conditions and is more likely to occur, is known as

a. Micro canonical Ensemble

b. Canonical Ensemble

c. Grand canonical Ensemble

d. Methods of most probable distribution

46: To find the statistical probability that a system will occupy one of the possible energy eigenvalues E_i, this task can be accomplished by means of

a. Micro canonical Ensemble

b. Canonical Ensemble

c. Grand canonical Ensemble

d. Methods of most probable distribution

47: The average energy can be expressed in term of partition function as follows

a. $E=\frac{\partial lnZ\left(\beta\right)}{\partial\beta}$

b. $\mathbf{E}=-\ \frac{\partial lnZ\left(\mathbf{\beta}\right)}{\partial\beta}$

c. $E=\frac{\partial lnZ\left(\beta,\gamma\right)}{\partial\beta}$

d. None

48: The diathermic walls in a canonical ensemble formulation are replaced by……in the grand canonical ensemble formulation

a. Adiabatic membranes

b. Semi-permeable membranes

c. Isothermal membranes

d. Semi-adiabatic membranes

49: The expression given by

a. Micro canonical partition function

b. Canonical partition function

c. Grand canonical partition function

d. None of these

50: Boltzmann distribution applies to those particles which are

a. Identical

b. Distinguishable

c. Both a and b

d. None

51: The dimensions of phase space volume are

a. (length x momentum)³

b. (work x time)³

c. (Angular momentum)³

d. (length)³

52: Most probable speed is

a. $\sqrt{\frac{3K_BT}{\pi m}}$

b. $\sqrt{\frac{3K_BT}{m}}$

c. $\sqrt{\frac{8K_BT}{\pi m}}$

d. $\sqrt{\frac{\mathbf{K}_\mathbf{B}\mathbf{T}}{\mathbf{m}}}$

54: Out of n particles in a gas, the number of particles having exactly the most probable velocity is

a. Zero

b. n

c. One

d. n/2

55: The probability that a molecule may have its x-component lying between is given by

a. $n\left(v_x\right)dv_x/n$

b. $\sqrt{\frac{m}{2\pi k_BT}}exp (-\frac{mv_x^2}{2k_BT})dv_x$

c. Both a and b

d. None of these

56: Experiments show that 1g mole of any dilute gas occupies the same molar volume given by

a. 2.24 X 10³cm³

b. 2.24 X 10⁴cm³

c. 2.24 X 10²cm³

d. 22.4 X 10⁴cm³

57: A gas can approach thermal equilibrium because of atomic collisions. The scattering cross-section between atoms is of order of where r₀ is effective atomic diameter given by

a. 10^-10cm

b. 10^-8cm

c. 10^-9cm

d. None of above

58: The ratio of molar volume to Avogadro’s number gives the density of any gas at S.T.P. Its value is

a. 2.7 X 10¹⁹atoms/cm³

b. 2.7 X 10¹⁸atoms/cm³

c. 3.7 X 10¹⁹atoms/cm³

d. None of these

59: In classical mechanics, the state of an atom at any instant of time is specified by its position and

a. Energy

b. Velocity

c. Momentum

d. All of these

60: For an isolated system, is constant overran energy surface, according to the argotic hypothesis. This condition is known as assumption of equal a priori probability and defines …….ensemble

a. Micro canonical

b. Canonical

c. Grand canonical

d. All of above

61: The entropy is defined to be proportional to logarithm of number of available states, which is measured by phase space volume in

a. µ space

b. Position space

c. Momentum space

d. T space

62: According to second law of thermodynamics, entropy of an isolated system can never

a. Decrease

b. Increase

c. Be zero

d. All of above

63: If a system has probable states labelled by and energy of state is E_i, then relative probability for finding the system in state is given by Boltzmann factor

a. $\mathbf{ \frac{e^\frac{-E_i}{K_BT}}{\sum_{i}e^\frac{-E_i}{K_BT}}}$

b. $\frac{{Ee}^\frac{E_i}{K_BT}}{\sum_{i} e^\frac{E_i}{K_BT}}$

c. $\frac{{E_ie}^\frac{E_i}{K_BT}}{\sum_{i} e^\frac{E_i}{K_BT}}$

d. None of above

64: The entropy of isolated system never decreases is imposed by the fact it is a monotonically increasing function of

a. Temperature

b. Volume

c. Pressure

d. All of above

65: The energy distribution function P(E) for a classical non-relativistic ideal gas, such that P(E)dE is the density of atoms with energy in range dE is

a. $\pi^{-\frac{1}{2}}(k_BT)^{-\frac{3}{2}}\sqrt E e^{-\frac{E}{k_BT}}$

b. $\mathbf{n\pi^{-\frac{1}{2}}(k_BT)^{-\frac{3}{2}}\sqrt Ee^{-\frac{E}{k_BT}}}$

c. $n\pi^{-\frac{1}{2}}(k_BT)^{-\frac{3}{2}}\sqrt E e^\frac{E}{k_BT}$

d. None of above

66: A gas in equilibrium has a distribution function, $\mathbf{f\left(p,r\right)=\frac{A(1+Bx)}{(2\pi m k_BT)^\frac{3}{2}}e^\frac{-p2}{2mk_BT}}$ A and B are constants and x is distance along an axis with a fixed origin. The nature of force acting on gas is

a. $\mathbf{A\left(1+Bx\right)=e^{-\frac{U}{k_BT}}}$

b. $A\left(1+Bx\right)=e^{-1}$

c. $A=e^{\frac{-U}{k_B}T}$

d. None of these

67: Suppose a surface of the container of a gas absorbs all molecules striking it with a normal velocity greater than v₀ . Absorption rate per unit area is

a. $\mathbf{n\sqrt{\frac{k_BT}{2\pi m}}e^\frac{-v_0^2}{2mk_BT}}$

b. $ne^\frac{-v_0^2}{2mk_BT}$

c. $n\sqrt{\frac{k_BT}{2\pi m}}$

d. All of above

68: The atmosphere contains molecules with high velocities that can escape the gravitational field of earth. The fraction of H₂ gas at sea level at 300K can escape from gravitational field of earth is

a. 4 X 10^-8

b. 5 X 10^-8

c. 4 X 10^-3

d. 5 X 10^-11

69: The volume element in phase space is product of a volume element in position space and volume element in ……….space

a. Momentum

b. Velocity

c. Gamma

d. mu

70: According to Maxwell-Boltzmann distribution, probability of a molecule to have zero speed is

a. Unity

b. 1/2

c. Nil

d. None of above

71: Particles which obey Pauli-Exclusion Principle are termed as

a. Maxwellians

b. Bosons

c. Fermions

d. None of these

72: According to Bose-Einstein Statistics, the probability of arranging particles with energy in cells for an N-particle system is given by

a. $\prod_{s}\frac{N!g_s^{n_s}}{n_s!}$

b. $\mathbf{\ \prod_{s}\frac{(n_s+g_s-1)}{n_s!\left(g_s-1\right)!}}$

c. $\prod_{s}\frac{{(g}_s)}{n_s!\left(g_s-n_s\right)!}$

d. $\prod_{s}\frac{{(g}_s)}{n_s!\left(g_s-n_s\right)!}$

73: The partition function is defined as

a. $\mathbf{\sum{g_ie^{(\frac{-E_i}{K_BT})}}}$

b. $\sum{g_ie^{(\frac{E_i}{K_BT})}}$

c. $\sum{g_ie^{(\frac{-\beta E_i}{K_BT})}}$

d. $\sum{g_ie^{(\frac{\beta E_i}{K_BT})}}$

74: The classical partition function is defined as

a. $Z=V(\frac{2\pi K_BT}{h^2})^\sfrac{3}{2}$

b. $\mathbf{Z=V(\frac{2\pi{\rm mK}_BT}{h^2})^\frac{3}{2}}$

c. $Z=V(\frac{2\pi K_BT}{h^2})^\frac{1}{2}$

d. None

75: According to theorem of Equipartition of energy the mean energy of a molecule of a gas is ……per degree of freedom

a. $\frac{5}{2}K_BT$

b. $\frac{3}{2}K_BT$

c. $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{K}_\mathbf{B}\mathbf{T}$

d. $\frac{-3}{2}K_BT$

76: The partition function for a Harmonic Oscillator is defined as

a. $Z=\sum_{n=0}^{\infty}{exp-(\frac{nhv}{K_BT}})$

b. $Z=\sum_{n=0}^{\infty}{exp-(\frac{(n-\frac{1}{2})hv}{K_BT}})$

c. $\mathbf{Z=\sum_{n=0}^{\infty}{exp-(\frac{(n+\frac{1}{2})hv}{K_BT}})}$

d. None

77: On the application of magnetic field H to a metal, those electrons whose spin magnetic moments are parallel to direction of applied field will possess a magnetic energy given by

a. ∆E=2μBH

b. ∆E=-2μBH

c. ∆E=μBH

d. ∆E=-μBH

78: The paramagnetic susceptibility of a metal according to Pauli is given by

a. $\chi=-\mu_B^2g[EF0]V$

b. $\chi=\mu_B^2g[EF0]V$

c. $\mathbf{\chi=-\mu_Bg[EF0]V}$

d. $\chi=\mu_Bg[EF0]V$

79: The average energy can be expressed in term of partition function as follows

a. $E=\frac{\partial lnZ(\beta)}{\partial\beta}$

b. $\mathbf{E}=-\frac{\partial lnZ(\mathbf{\beta})}{\partial\beta}$

c. $E=\frac{\partial lnZ(\beta,\gamma)}{\partial\beta}$

d. None

80: The average pressure can be expressed in term of partition function as follows

a. $P=\frac{\partial lnZ(\beta)}{\partial V}$

b. $\mathbf{P}=-\frac{\partial lnZ(\mathbf{\beta})}{\partial V}$

c. $P=\frac{\partial lnZ(\beta)}{\partial\beta}$

d. $P=-\frac{\partial lnZ(\beta)}{\partial\beta}$

81: Particles which have zero spin/integral spin and do not obey Pauli-Exclusion Principle are termed as

a. Maxwellian

b. Bosons

c. Fermions

d. None of them

82: According to Fermi-Dirac Statistics, the probability of arranging particles with energy in cells for an N-particle system is given by

a. $\ \prod_{s}\frac{N!g_s^{n_s}}{n_s!}$

b. $\prod_{s}\frac{(n_s+g_s-1)}{n_s!\left(g_s-1\right)!}$

c. $\prod_{\mathbf{s}}\frac{{(\mathbf{g}}<em>\mathbf{s})}{\mathbf{n}</em>\mathbf{s}!\left(\mathbf{g}<em>\mathbf{s}-\mathbf{n}</em>\mathbf{s}\right)!}$

d. $\prod_{s}\frac{(n_s+g_s+1)}{n_s!\left(g_s+1\right)!}$

83: For indistinguishable particles, it is difficult to say which particle is in which one-particle eigenstate, so to find the number of microstates one can consider the ……statistics, according to which ‘’any one-particle eigenstate can be occupied by any number of particles

a. Maxwell-Boltzmann

b. Bose-Einstein

c. Fermi-Dirac

d. None of them

84: To arrange particles with energy in cells, the number of arrangements of particles among themselves will be given by

a. $g_i!$

b. $\ \mathbf{n}_\mathbf{i}!$

c. $\ {(g}_i-n_i)!$

d. $\left(n_i+g_i-1\right)!$

85: For indistinguishable particles, it is difficult to say which particle is in which one-particle eigenstate, so to find the number of microstates one can consider the ……statistics, according to which ‘’any one-particle eigenstate can be occupied by only zero or one particle

a. Maxwell-Boltzmann

b. Bose-Einstein

c. Fermi-Dirac

d. None

86: The ratio of emissive power to absorptive power of a perfect black body of all bodies at a given temperature is same and is equal to the emissive power of a perfect black body. This is known as

a. Rayleigh-Jeans Law

b. Plank’s Law

c. Stefan’s Law

d. Kirchhoff’s Law

87: As photons may be absorbed or reemitted by the walls of the black body, the number of photons inside the enclosure is not fixed. As a result, we can take the value of α equal to

a. Zero

b. Unity

c. Infinity

d. None of them

88: The Fermi-energy of the electron gas can be expressed in term of thermal energy by defining a Fermi temperature as follows

a. ${\ \ k}_BT_F{=E}_F(0)$

b. ${\ k}_B^2T_F{=E}_F(0)$

c. $-k_B{TT}_F{=E}_F(0)$

d. None of them

89: For energy of electrons E< (0), the value of Fermi function is given by

a. f(E)=0

b. f(E)=1

c. f(E)=∞

d. None of them

90: Degeneracy temperature is given by

a. $(\frac{\mathbf{h}^\mathbf{2}}{\mathbf{2\pi m}\mathbf{k}_\mathbf{B}})\mathbf{n}^\frac{\mathbf{2}}{\mathbf{3}}$

b. $(\ \frac{h^2}{2\pi m k_B})n^\frac{3}{2}$

c. $(\ \frac{h}{2\pi m k_B}{)^\frac{2}{3}n}^\frac{2}{3}$

d. None of them

91: A condition defines a line in Tn-plane that serves a rough division between classical and quantum regimes is given by

a. $n\lambda^3<1$

b. $n\lambda^3>1$

c. $n\lambda^3\ll1$

d. $\mathbf{n}\mathbf{\lambda}^\mathbf{3}\cong\mathbf{1}$

92: Permutation operator commutes with Hamiltonian. From this we infer the result that permutation operator is

a. Identity operator

b. Projection operator

c. Constant of motion

d. Null matrix

93: The Bose-Einstein condensation of an ideal gas is one of few examples of a phase transition that can be described completely in term of …….physics

a. Microscopic

b. Macroscopic

c. Classical

d. Electrical

94: In which statistics, occupation index n can tend to zero

a. Maxwell-Boltzmann

b. Fermi-Dirac

c. Bose-Einstein

d. None

95: The average energy of an electron in Fermi gas is

a. $\frac{\ \ \mathbf{3}\mathbf{\varepsilon}_\mathbf{F}}{\mathbf{5}}$

b. $\frac{3N\varepsilon_F}{5}$

c. $\frac{2\varepsilon_F}{5}$

d. None of above

96: The two fermions wave function is

a. $\mathbf{\Psi=\frac{1}{\sqrt2}{\Psi\left(1,2\right)-\Psi\left(2,1\right)} }$

b. $\mathrm{\Psi}=\frac{1}{\sqrt2}{\mathrm{\Psi}\left(1,2\right)+\mathrm{\Psi}\left(2,1\right)}$

c. Both a & b

d. None

97: The wave function of two systems of identical, non-interacting particles: the 1^st consists of two bosons is

a. $\mathbf{\Psi_S=\frac{1}{\sqrt2}{_{{\Psi_1\left(1\right)\Psi_2\left(2\right)+\Psi_1\left(2\right)\Psi_2\left(1\right)}x_s}^{{\Psi_1\left(1\right)\Psi_2\left(2\right)-\Psi_1\left(2\right)\Psi_2\left(1\right)}x_a}}}$

b. $\Psi_S=\frac{1}{\sqrt2}{_{{\Psi_1\left(1\right)\Psi_2\left(2\right)+\Psi_1\left(2\right)\Psi_2\left(1\right)}x_s}^{{\Psi_1\left(1\right)\Psi_2\left(1\right)-\Psi_1\left(2\right)\Psi_2\left(1\right)}x_a}}$

c. Both a&b

d. None of above

98: For a system of three non-interacting particles, the symmetric wave function is given by:

a. $\mathbf{\Psi_S\left(1,2,3\right)=\frac{1}{\sqrt{3!}} \sum_{p}^{}p' \Psi_1(1)\Psi_2{\left(2\right)\Psi}_3(3)}$

b. $\Psi_S\left(1,2,3\right)=\frac{1}{\sqrt{3!}} \sum_{p}^{}p' \Psi_1(2)\Psi_2{\left(2\right)\Psi}_3(3)$

c. Both a&b

d. None of above

100: Fermi-Dirac statistics assumes that the particles of system are identical and

a. Distinguishable

b. Indistinguishable

c. Both a&b

d. Obey boyle’s law

101: Total number of Fermions in a system is

a. Constant

b. Infinity

c. Not constant

d. None of above

102: The energy value up to which all energy states are full at 0K and above which all energy states are empty is known as

a. Maximum energy

b. Zero point energy

c. Ground state energy

d. Fermi energy

103: According to Plank, energy of oscillator is given by

a. $\mathbf{E=nhv,\ n=1,2,3,\ldots}$

b. $E=hv,\ n=1,2,3,\ldots$

c. $E=ngh,\ n=1,2,3,\ldots$

d. All of above

104: The wavelength of emitted radiation of maximum intensity is inversely proportional to absolute temperature. This is known as

a. Stefan’s law

b. Rayleigh-Jeans law

d. Wien’s displacement law

d. Plank’s quantum law

105: Plank received Nobel Prize in physics for his introduction of the quantum concept and explanation of black body spectrum in

a. 1910

b. 1918

c. 1915

d. None of above

106: Black body can be made by

a. A tungsten filament

b. A highly polished black body

c. A hollow cavity within a solid body

d. None of above

107: An ideal black body is

a. A perfect absorber of radiation

b. The most efficient radiator

c. A body whose absorptive power is unity

d. All of above

108: Radiations are always emitted or absorbed in the form of packets of energy. This is statement of

a. Stefan’s law

b. Rayleigh-Jeans law

c. Plank’s quantum law

d. Wien’s displacement law

109: As the temperature of black body is raised, the wavelength corresponding to maximum intensity

a. Shifts toward longer wavelength

b. Remains same

c. Shifts toward shorter wavelength

d. None of above

110: The radiations emitted by a hot body at different temperatures are

a. With discontinuous range of wavelength

b. With continuous range of wavelength

c. Both a&b

d. with infinite range of wavelengths

111: Experiments have shown that neither free expansion nor …………result in change of temperature of an ideal gas

a. Adiabatic process

b. Virial expansion

c. Compacting process

d. Throttling process

112: The relation for the Virial expansion is given by ( p = N/V )

a. $P=k_BT[\ \rho+B_2\rho^2+B_3\rho^3+\ldots]$

b. $P=k_BT_\rho[\ 1+B_2\rho^1+B_3\rho^2+\ldots]$

c. $\mathbf{\frac{P}{k_BT}=\rho[1+B_2\left(T\right)\rho+B_3\left(T\right)\rho^2+\ldots]}$

d. None of these

113: The relation for Virial expansion transforms to ideal gas equation of state, if

a. $B_3\left(T\right)=0$

b. $B_2\left(T\right)=0$

c. $B_1\left(T\right)=0$

d. $\mathbf{B_2\left(T\right)=B_3\left(T\right)=0}$

114: In the Vander Waals equation of state, the constant ‘a’ accounts for

a. The long range weakly interactive forces

b. Four times the single molecule volume

c. The short range weakly interactive forces

d. Twice the single molecule volume

115: In the Vander Waals equation of state, the constant ‘b’ accounts for

a. The long range weakly interactive forces

b. Four times the single molecule volume

c. The short range weakly interactive forces

d. Twice the single molecule volume

116: For a system of N-molecules, there will be the total pair interactions of

a. $\ \frac{N(N+1)}{2}$

b. $\mathbf{\frac{N(N-1)}{2}}$

c. $\frac{N(N^2+1)}{2}$

d. $\frac{N(N^2-1)}{2}$

117: In the term $\mathbf{-\epsilon(\frac{\sigma}{r})^s}$ a good approximation for the exponent s is

a. s = 3

b. s = 4

c. s = 5

d. s = 6

118: Approximating an interacting system by a non-interacting one in a self-consistent external field which is expressed in terms of an order parameter is known as

a. Bragg-Williams Approximation

b. Weiss Molecular Field Approximation

c. Effective Potential Approximation

d. Hard-sphere Potential Approximation

119: The ability of body to radiate is related to its ability to…..radiation

a. Emit

b. Absorb

c. Pass

d. None

120: One trivial solution for the equation $m=\sigma=\tan{h(\beta qJm)}$ is

a. m=0

b. m=1

c. m=2

d. m=3

121: At ordinary temperature, contribution of electronic heat capacity to the heat capacity of solids is

a. Small

b. Infinite

c. Large

d. Cannot be predicted

122: In Einstein theory of specific heat of solids, the atoms in solid are assumed as

a. Coupled oscillator

b. Independent oscillator

c. Damped oscillator

d. None of above

123: Lattice vibrations are

a. Longitudinal

b. Transverse

c. Both a and b

d. None of these

124: The momentum of phonon is

a. $\mathbf{\hbar k^\rightarrow}$

b. $\hbar \omega$

c. Zero

d. None of these

125: Energy of elastic waves is always

a. Zero

b. Continuous

c. Quantized

d. Cannot be predicted

126: According to Einstein model, as temperature approaches to zero, lattice contribution to heat capacity of solid approaches to

a. Infinity

b. Zero

c. Any value

d. Constant large value

127: The assumption that the atoms in a lattice are coupled together is taken into account for variation of heat capacity of solid by

a. Dulong and Petit

b. Einstein

c. Debye

d. All of above

128: For what value of k stationary waves are set up in one dimensional lattice?

a. $\mathbf{k=\pi/a}$

b. $k=2\pi/a$

c. $k\rightarrow0$

d. $k=4\pi/a$

130: The quantum energy associated with an elastic wave is called

a. Photon

b. Neutron

c. Phonon

d. All of above

131: The concept of quantized lattice vibrations helps to explain a number of properties of solids such as………near absolute zero

a. Volume of solid

b. Pressure of solid

c. Heat capacity

d. All of above

132: The velocity with which the wave crests and troughs travel through a medium is called

a. Group velocity

b. Phase velocity

c. Uniform velocity

d. Average velocity

133: A phonon is emitted or absorbed in ……….scattering of photon by crystal

a. Elastic

b. Inelastic

c. Both a and b

d. None of above

134: Dulong and Petit law fails at

a. Low temperature

b. High temperature

c. Both a and b

d. None of these

135: The density matrix expresses the result of taking quantum mechanical matrix elements and ensemble averages in ………..operation

a. Different

b. Same

c. Both a and b

d. None of these

136: If we have some type of wave like excitations in a solid with dispersion relation ω=ak² . Then excitation makes a contribution to total heat capacity proportional to

a. T³

b. T²

c. T^3/2

d. None of above

137: The molecules in an ordinary gas which have integral angular momentum in units of h/2π are termed as

a. Maxwellians

b. Bosons

c. Fermions

d. None of these

138: According to F. London, Liquid …………displays phenomena similar to Bose-Einstein condensation of a perfect BE gas

a. Helium-2(²He)

b. Helium-3(³He)

c. Helium-4(⁴He)

d. None of these

139: The process of concentrating particles into the zero-energy ground state is known as

a. Vaporization

b. Bose-Einstein condensation

c. Throttling process

d. None

140: At T=4K, the factor e^-α is approximately equal to

a. 3 x 10^-6

b. 2.61

c. 1.93

d. 0.15

141: The value of experimental lambda point for helium is

a. 4.20K

b. 3.13K

c. 2.17K

d. None of these

142: According to quantum mechanics, an observable is associated with…….that operates on a Hilbert space

a. Wave-function

b. Eigenvector

c. Hermitian operator

d. None of these

143: According to postulate of random phases, the state of system may be regarded as

a. An incoherent superposition of eigenstates

b. A coherent superposition of eigenstates

c. A consistent superposition of eigenstates

d. None of these

144: Phases of the complex numbers{b_n} are………..,since $\mathbf{\mathrm{\Psi}=\sum_{n}{b_n\phi_n}}$

a. Random number

b. Random phases

c. Incoherent

d. Superposition of states

145: If $\mathbf{\rho_{mn}=\delta_{mn}|b_n|^2}$ then $\mathbf{\rho_{mn}}$ is

a. An identity matrix

b. An inverse matrix

c. A null matrix

d. A diagonal matrix

146: The equation of motion for density operator ρ is $\mathbf{ih\frac{\partial p}{\partial t}=[H,\rho] }$ and if Hamiltonian H is time independent and ρ commute with H, then ρ will be

a. Time independent

b. Time dependent

c. Commutator

d. Non-commutator

147: The equilibrium macro state of a system corresponds to state of:

a. Maximum probability

b. Minimum probability

c. Ordered state

d. All of these

148: The particles obeying Fermi-Dirac statistics have spin:

a. Integral

b. Half integral

c. Zero

d. None

149: The particles which are identical, indistinguishable and have integral spin are called:

a. Bosons

b. Fermions

c. Phonons

d. All of these

150: The dimensions of phase space volume are:

a. $\left(length\timesmomentum\right)^3$

b. $\left(work\times t i m e\right)^3$

c. $\left(angular\ momentum\right)^3$

d. $\left(length\right)^3$

151: Statistical methods give greater accuracy when number of observation is:

a. Very small

b. Very large

c. Neither very small nor very large

d. None

152: The macro states which are allowed under a constraint are called……. Macro states:

a. Particular

b. Inaccessible

c. Accessible

d. None

153: In Maxwell-Boltzmann statistics particles are treated as:

a. Distinguishable

b. Indistinguishable

c. Photons

d. None

154: Free electrons in metals obey……………….. statistics:

a. Maxwell-Boltzmann

b. Classical

c. Fermi-Dirac

d. Bose-Einstein

155: Minimum size of cell in quantum statistics is:

a. $\mathbf{h^3}$

b. $\hbar^3$

c. Zero

d. None

156: Molecules of N₂ at S.T.P. obey ………. Statistics:

a. Maxwell-Boltzmann

b. Classical

c. Fermi-Dirac

d. Bose-Einstien

157: The value of γ for a gas is 1.66, then gas is:

a. O₂

b. H₂

c. Ne

d. N₂

158: The dimensions of universal gas constant are:

a. $\left[M^2L^2T^{-2}\right]$

b. $\mathbf{\left[ML^2T^{-2}\right]}$

c. $\left[MLT^{-2}\right]$

d. $\left[MLT\right]$

159: The temperature which is same in ^oC and ^oF is:

a. $-40^0 F$

b. $40^0 F$

c. $-20^0 F$

d. $20^0 F$

160: At which temperature do the Fahrenheit and Kelvin scales coincide:

a. $273^0 F$

b. $-100^0 F$

c. $\mathbf{574^0 F}$

d. $844^0 F$

161: Absolute temperature can be calculated by:

a. Mean square speed

b. Motion of molecules

c. a & b

d. Amplitude

162: When the temperature difference between the source and sink increases, the efficiency of heat engine will:

a. Decrease

b. Increase

c. Is not affected

d. None

163: The thermodynamic temperature scale was given by:

a. Kelvin

b. Fahrenheit

c. Dewar

d. Carnot

164: A Carnot engine can be 100% efficient if LTR is at:

a. 0^oC

b. 0K

c. 0^oF

d. 273K

165: A piece of ice is at 0^oC dropped into water at 0^oC the ice will be:

a. Melt

b. Partially melt

c. Not melt

d. Be converted into water

166: In free expansion of gas the internal energy of system:

a. Decreases

b. Unchanged

c. Changes

d. Increases

167: The dimensions of phase space volume are:

a. $\mathbf{\left(length\times m o m e n t u m\right)^3}$

b. $\left(work\times t i m e\right)^3$

c. $\left(angular\ momentum\right)^3$

d. $\left(length\right)^3$

168: The most probable speed is:

a. $\sqrt{\frac{3k_BT}{\pi m}}$

b. $\sqrt{\frac{3k_BT}{m}}$

c. $\sqrt{\frac{8k_BT}{\pi m}}$

d. $\sqrt{\frac{k_BT}{m}}$

169: Out of n particles in a gas, the number of particles having exactly the most probable velocity is:

a. Zero

b. n

c. One

d. n/2

170: The probability that a molecule may have its x-component lying between vx and v_x+dv_x is given by:

a. $\frac{n\left(v_x\right)dv_x}{n}$

b. $\sqrt{\frac{m}{2\pi k_BT}e\left(-\frac{mv_x^2}{2k_BT}\right)dv_x}$

c. a & b

d. None

171: Experiments show that 1g mole of any dilute gas occupies the same molar volume given by:

a. $2.24\times{10}^3cm^3$

b. $\mathbf{2.24\times{10}^4cm^3}$

c. $2.24\times{10}^2cm^3$

d. $22.4\times{10}^3cm^3$

172: A gas can approach thermal equilibrium because of atomic collisions. The scattering cross-section between atoms is of order of $\pi r_o^2$ , where r_o is effective atomic diameter given by:

a. ${10}^{-10}cm$

b. $\mathbf{{10}^{-8}cm}$

c. ${10}^{-9}cm$

d. None

173: The ratio of molar volume to Avogadro number gives the density of any gas at S.T.P. Its value is:

a. $\mathbf{2.7\times{10}^{19}\ atoms/cm^3}$

b. $2.7\times{10}^{18}\ atoms/cm^3$

c. $3.7\times{10}^{19}\ atoms/cm^3$

d. None

174: In classical mechanics the state of an atom at any instant of time is specified by its position and:

a. Energy

b. Velocity

c. Momentum

d. All of these

175: For an isolated system, p is a constant over an energy surface, according to the Ergodic hypothesis. This condition is known as consumption of an equal priori probability and defines…….. ensembles:

a. Micro canonical

b. Canonical

c. Grand canonical

d. All of these

176: The entropy is defined to be proportional to logarithm of number of available states, which is measured by phase space volume in:

a. µ-Space

b. Position space

c. Momentum space

d. t -space

177: According to 2^nd law of thermodynamics, entropy of an isolated system can never:

a. Decrease

b. Increase

c. Zero

d. All of these

178: If a system has probable states labeled by i and energy of state i is E_i, then relative probability for finding the system in state is given by Boltzmann factor:

a. $\mathbf{\frac{e^{-\frac{E_i}{k_BT}}}{\sum_{i} e^{-\frac{E_i}{k_BT}}}}$

b. $E\frac{e^{-\frac{E_i}{k_BT}}}{\sum_{i} e^{-\frac{E_i}{k_BT}}}$

c. $E_i\frac{e^{-\frac{E_i}{k_BT}}}{\sum_{i} e^{-\frac{E_i}{k_BT}}}$

d. None

179: The entropy of an isolated system never decreases is implied by fact it is a monotonically increasing function of:

a. Temperature

b. Volume

c. Pressure

d. All of these

180: The equilibrium macro state of a system corresponds to a state of:

a. Maximum probability

b. Minimum probability

c. Ordered state

d. None

181: The particles obeying Fermi-Dirac statistics have spin:

a. Integral

b. Zero

c. Half integral

d. None

182: The particles which are identical, indistinguishable and have integral spins are called:

a. Fermions

b. Bosons

c. Phonons

d. Photons

183: Approximately at what density in molecules/m³ does mean free path of nitrogen molecules equals the size of a room about 3m:

a. ${10}^9$

b. ${10}^{18}$

c. ${10}^{20}$

d. ${10}^{23}$

184: The most probable speed is given by:

a. $\mathbf{\sqrt{\frac{2k_BT}{m}}}$

b. $\sqrt{\frac{8k_BT}{m}}$

c. $\sqrt{\frac{3k_BT}{m}}$

d. $2\sqrt{\frac{3k_BT}{m}}$

185: For a gas at N.T.P. which will be maximum:

a. $v_{av}$

b. $\mathbf{v_{rms}}$

c. $v_{mp}$

d. None

186: Out of n particles the number of particles having exactly the most probable velocity is:

a. n

b. 1

c. zero

d. $\frac{n}{2}$

187: Plank’s formula for black body radiation can be derived from statistics:

a. Fermi-Dirac statistics

b. Bose-Einstein statistics

c. Maxwell-Boltzmann statistics

d. Goldstein

188: Pauli exclusion principle applies to:

a. Fermions

b. Bosons

c. Phonons

d. Photons

189: The average energy of an electron in Fermi gas at 0K is:

a. $0.2E_F$

b. $0.8E_F$

c. $0.4E_F$

d. $\mathbf{0.6E_F}$

190: For a gas enclosed in a container consists of a mixture of Helium and krypton. This mixture can be treated as an ideal gas if it is assumed that both types of atoms have same:

a. Speed

b. Kinetic energy

c. Momentum

d. Mass

191: The number of arrangements of six distinguishable particles among 4 cells of equal a priori probability there being no restriction on number of particles entering into cell is:

a. 30

b. 84

c. 24

d. 210

192: The wavelength at which black body emits maximum amount of radiation is proportional to:

a. T

b. $\mathbf{ \frac{1}{T}}$

c. $T^4$

d. $T^2$

193: A card is drawn from a pack of 52. The probability of its being an ace or king is:

a. $\frac{2}{52}$

b. $\frac{4}{52}$

c. $\frac{\mathbf{8}}{\mathbf{52}}$

d. None

194: Constraints imposed on a system :

a. Decreases number of inaccessible states

b. Increases number of inaccessible states

c. Sometimes a & sometimes b

d. Have no effect

194: The probability of an event can never be:

a. Zero

b. 1

c. Negative

d. 1/2

195: Statistical methods give greater accuracy when number of observations is:

a. Very small

b. Very large

c) Neither very small nor very large

d. None

196: The macro states which are allowed under a constraint are called………… macro states:

a. Particular

b. Inaccessible

c. Accessible

d. None

197: n- similiar coins are tossed simultaneously for a large number of times then probability of r-heads uppermost is:

a. $\frac{n!}{r!\left(n-r\right)!}\frac{1}{2^n}$

b. $\frac{n!}{r!\left(n-r\right)!}$

c. $\frac{n!}{\left(n-r\right)!}\frac{1}{2^n}$

d. None

198: Which of the following is not example of Bosons:

a. Mesons

b. Helium

c. Electron

d. Photons

199: According to statistics entropy is a measure of molecular arrangement:

a. Ordered

b. Disordered

c. Uniformly

d. None

200: Which of the following cases do not correspond to behavior of an ideal gas:

a. Collision can change internal energy of molecules

b. A molecule loses kinetic energy when it collides elastically with another molecule

c. The speed of molecule is unchanged after a collision with walls of container

d. There is potential energy associated with interactions between molecules

201: A vessel contains 1 mole of O2 at a temperature T the pressure is P. An ideal vessel containing 1 mole of He gas at a temperature 2T has a pressure:

a. P

b. P/8

c. 2P

d. 8P

202: The temperature of an ideal gas is increased from 120K to 480K. If at 120K rms velocity of a gas is v at 480K it becomes:

a. 4v

b. 2v

c. v/4

d. v/2

202: Two gases having same pressure P and volume V are mixed at a temperature T . If mixture is at a temperature I and occupies same volume V, then pressure of mixture would be:

a. P

b. 3P

c. 2P

d. P/2

203: Find amount of work done to increase the temperature of 1 mole of an ideal gas by 30^oC if it is expanding under the condition $V\propto T^\frac{2}{3}$ :

a. 126.2J

b. 136.2J

c. 166.2J

d. Unpredictable

204: The internal energy of one mole of an ideal gas depends on:

a. Pressure

b. Temperature

c. Volume

d. Temperature and pressure

205: The amount of heat required to increase the temperature of 1 mole of a triatomic gas at constant volume is in n – times the amount of heat required for 1 mole of monoatomic gas. The value of n will be:

a. 1,3

b. 2

c. 1,5

d. 1

206: If number of gas molecules in a cubical vessel is increased from N to 3N, then its pressure and total energy will be:

a. Four times

b. Double

c. Three times

d. Half

207: The temperature at which rms speed of gas molecules become double its value at 0^oC is:

a. 760^oC

b. 819oC

c. 273^oC

d. 100^oC

MCQ's with Answers

1: What survives the averaging in the measurements of an observable?

2: A system is in thermodynamic equilibrium if it satisfies the stringent requirements of

3: For a simple enclosed in adiabatic walls, the only permissible form of energy transfer is

4: Entropy ‘S’ vanishes if

5: The coefficient of thermal expansion (expansivity) β is defined as

6: Cp-Cv is equal to

8: The Maxwell relation is given by

9: Which one of the following is not a thermodynamic potential

10: Sublimation is an example of phase transition known as

11: The equilibrium state (macro-state) of a system corresponds to state of

12: The particles obeying Fermi-Dirac statistics have spin

13: The particles which are identical, indistinguishable and have integral spin are called

14: The dimensions of phase space volume are

15: Statistical methods give greater accuracy when number of observations is

16: The macro-states which are allowed under a constraint are called ……macro-states

17: In Maxwell-Boltzmann statistics , particles are treated as

18: Free electrons in metals obey ………statistics

19: Minimum size of a cell in quantum statistics is

20: Molecules of N2 at S.T.P. obey ………statistics

21: The value of γ for a gas is 1.66, then gas is

22: The dimensions of universal gas constant R is

23: The temperature which is same in and is

24: At what temperature do the Fahrenheit and kelvin scales coincide?

25: Absolute temperature can be calculated by

26: When the temperature difference between the source and sink increases, the efficiency of heat engine will

27: The thermodynamic temperature scale was given by

28: A Carnot engine can be 100% efficient if LTR is at

29: A piece of ice at 0 is dropped into water at 0 the ice will

30: In free expansion of gas the internal energy of system

31: A random variable x has a set of possible outcomes, which may be

32: The probability is always

33: The Normalization of probability requires that

34: Objective probabilities are obtained through

35: The cumulants are the generator of

36: The characteristic function is the generator of

37: The expectation values for powers of a random variable are known as

38: The Mean value for Gaussian distribution is given by

39: The Mean value for a Poisson distribution is given by

40: The Poisson distribution can be taken as

41: Particles which obey Pauli-Exclusion Principle are termed as

42: At least, how many macroscopic observables are required to specify the state of a system

43: A state where all the parameters of the constituent particles are specified is called

44: The statistical weight represents the number of

45: To find a Microstate which contains a large number of microstates, represents thermodynamic equilibrium conditions and is more likely to occur, is known as

46: To find the statistical probability that a system will occupy one of the possible energy eigenvalues Ei, this task can be accomplished by means of

47: The average energy can be expressed in term of partition function as follows

48: The diathermic walls in a canonical ensemble formulation are replaced by……in the grand canonical ensemble formulation

49: The expression given by

50: Boltzmann distribution applies to those particles which are

51: The dimensions of phase space volume are

52: Most probable speed is

54: Out of n particles in a gas, the number of particles having exactly the most probable velocity is

55: The probability that a molecule may have its x-component lying between is given by

56: Experiments show that 1g mole of any dilute gas occupies the same molar volume given by

57: A gas can approach thermal equilibrium because of atomic collisions. The scattering cross-section between atoms is of order of where r0 is effective atomic diameter given by

58: The ratio of molar volume to Avogadro’s number gives the density of any gas at S.T.P. Its value is

59: In classical mechanics, the state of an atom at any instant of time is specified by its position and

60: For an isolated system, is constant overran energy surface, according to the argotic hypothesis. This condition is known as assumption of equal a priori probability and defines …….ensemble

61: The entropy is defined to be proportional to logarithm of number of available states, which is measured by phase space volume in

62: According to second law of thermodynamics, entropy of an isolated system can never

63: If a system has probable states labelled by and energy of state is Ei, then relative probability for finding the system in state is given by Boltzmann factor

64: The entropy of isolated system never decreases is imposed by the fact it is a monotonically increasing function of

65: The energy distribution function P(E) for a classical non-relativistic ideal gas, such that P(E)dE is the density of atoms with energy in range dE is

67: Suppose a surface of the container of a gas absorbs all molecules striking it with a normal velocity greater than v0 . Absorption rate per unit area is

68: The atmosphere contains molecules with high velocities that can escape the gravitational field of earth. The fraction of H2 gas at sea level at 300K can escape from gravitational field of earth is

69: The volume element in phase space is product of a volume element in position space and volume element in ……….space

70: According to Maxwell-Boltzmann distribution, probability of a molecule to have zero speed is

71: Particles which obey Pauli-Exclusion Principle are termed as

72: According to Bose-Einstein Statistics, the probability of arranging particles with energy in cells for an N-particle system is given by

73: The partition function is defined as

74: The classical partition function is defined as

75: According to theorem of Equipartition of energy the mean energy of a molecule of a gas is ……per degree of freedom

76: The partition function for a Harmonic Oscillator is defined as

77: On the application of magnetic field H to a metal, those electrons whose spin magnetic moments are parallel to direction of applied field will possess a magnetic energy given by

78: The paramagnetic susceptibility of a metal according to Pauli is given by

79: The average energy can be expressed in term of partition function as follows

80: The average pressure can be expressed in term of partition function as follows

81: Particles which have zero spin/integral spin and do not obey Pauli-Exclusion Principle are termed as

82: According to Fermi-Dirac Statistics, the probability of arranging particles with energy in cells for an N-particle system is given by

6: C_p-C_v is equal to

20: Molecules of N₂at S.T.P. obey ………statistics

46: To find the statistical probability that a system will occupy one of the possible energy eigenvalues E_i, this task can be accomplished by means of

57: A gas can approach thermal equilibrium because of atomic collisions. The scattering cross-section between atoms is of order of where r₀ is effective atomic diameter given by

63: If a system has probable states labelled by and energy of state is E_i, then relative probability for finding the system in state is given by Boltzmann factor

67: Suppose a surface of the container of a gas absorbs all molecules striking it with a normal velocity greater than v₀ . Absorption rate per unit area is

68: The atmosphere contains molecules with high velocities that can escape the gravitational field of earth. The fraction of H₂ gas at sea level at 300K can escape from gravitational field of earth is

97: The wave function of two systems of identical, non-interacting particles: the 1^st consists of two bosons is

136: If we have some type of wave like excitations in a solid with dispersion relation ω=ak² . Then excitation makes a contribution to total heat capacity proportional to

140: At T=4K, the factor e^-α is approximately equal to