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: Cp-Cv 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 N2 at 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 Ei, 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 103 cm3
b. 2.24 X 104 cm3
c. 2.24 X 102 cm3
d. 22.4 X 104 cm3
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 Ei, 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. $\prod_{\mathbf{s}}\frac{{(\mathbf{g}}\mathbf{s})}{\mathbf{n}\mathbf{s}!\left(\mathbf{g}\mathbf{s}-\mathbf{n}\mathbf{s}\right)!}$
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 1st 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. T3/2
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{bn} 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. 0oC
b. 0K
c. 0oF
d. 273K
165: A piece of ice is at 0oC dropped into water at 0oC 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 vx+dvx 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 ro 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 2nd 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 Ei, 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 30oC 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 0oC is:
a. 760oC
b. 819oC
c. 273oC
d. 100oC
