In microcanonical ensemble, all accessible microstates have
A Different probabilities
B Zero probability
C Equal probabilities
D Probabilities depending on temperature
All microstates with same E, V, N are equally likely.
Canonical ensemble describes a system in thermal contact with reservoir maintaining
A Constant T
B Constant μ
C Constant P
D Constant entropy
Grand canonical ensemble allows exchange of
A Only energy
B Only particles
C Energy and particles
D Only volume
Chemical potential enters FD and BE distributions through the term
A e(E+μ)/kTe^{(E+\mu)/kT}e(E+μ)/kT
B e(E−μ)/kTe^{(E-\mu)/kT}e(E−μ)/kT
C eμ/kTe^{\mu/kT}eμ/kT
D μ does not appear
Fermi temperature TFT_FTF relates to
A Planck constant
B Fermi energy EF=kBTFE_F = k_B T_FEF=kBTF
C Only Maxwell distribution
D Heat capacity
At T = 0 K, the Fermi–Dirac distribution becomes
A A step function
B A delta function
C A Gaussian
D A linear function
Heat capacity of a degenerate Fermi gas at low temperature varies as
A T
B T²
C 1/T
D Constant
Because only electrons near EF contribute.
Bose–Einstein condensation happens when
A µ → 0⁺
B µ → lowest energy level (ground-state energy)
C µ becomes very large
D µ becomes negative infinity
Photon gas has chemical potential
A Positive
B Negative
C Zero
D Infinite
Partition function Z for a system is related to Helmholtz free energy F by
A F=kTlnZF = kT \ln ZF=kTlnZ
B F=−kTlnZF = -kT \ln ZF=−kTlnZ
C F=Z/kTF = Z/kTF=Z/kT
D F=kTZF = kT ZF=kTZ
Entropy in canonical ensemble can be obtained from
A S=−(∂F/∂T)VS = -\left(\partial F/\partial T\right)_VS=−(∂F/∂T)V
B S=F/TS = F/TS=F/T
C S=PV/TS = PV/TS=PV/T
D S=μ/TS = \mu/TS=μ/T
The Maxwell relation from U(S,V):
A (∂T∂V)S=(∂P∂S)V\left(\frac{\partial T}{\partial V}\right)_S = \left(\frac{\partial P}{\partial S}\right)_V(∂V∂T)S=(∂S∂P)V
B P=−(∂F∂V)TP = -\left(\frac{\partial F}{\partial V}\right)_TP=−(∂V∂F)T
C μ=(∂G∂N)T,P\mu = \left(\frac{\partial G}{\partial N}\right)_{T,P}μ=(∂N∂G)T,P
D H=U+PVH = U + PVH=U+PV
Thermodynamic identity for U is
A dU = TdS – PdV
B dU = SdT – VdP
C dU = PdV
D dU = TdP
Irreversibility in thermodynamics corresponds to
A Decrease in entropy
B Increase in entropy
C Constant entropy
D Zero temperature
For a reversible isothermal expansion of an ideal gas, ΔS equals
A 0
B nRln(Vf/Vi)nR \ln(V_f/V_i)nRln(Vf/Vi)
C −nRln(Vf/Vi)-nR \ln(V_f/V_i)−nRln(Vf/Vi)
D Infinity
A lightlike spacetime interval satisfies
A s2>0s^2 > 0s2>0
B s2<0s^2 < 0s2<0
C s2=0s^2 = 0s2=0
D s² imaginary
A 4-vector transforms
A Under Galilean rules
B Under Lorentz transformation
C Under Newtonian relativity
D Does not transform
The spacetime interval is invariant under Lorentz transformations. Which statement is true?
A Observers disagree on s²
B All observers agree on s²
C s² = 0 always
D s² only defined for massive particles
In relativity, momentum and energy form
A A scalar
B A 3-vector
C A 4-vector (E/c,p)(E/c, \mathbf{p})(E/c,p)
D A tensor of rank 2
Proper time interval dτ between events on a worldline is related by
A dτ=dtd\tau = dtdτ=dt
B dτ=dt/γd\tau = dt/\gammadτ=dt/γ
C dτ=γdtd\tau = \gamma dtdτ=γdt
D dτ=cdtd\tau = cdtdτ=cdt
Time dilation factor is
A γ
B 1/γ
C γ²
D 0
If Δx = 0 for two events in an observer’s frame, that time interval is
A Not proper
B Proper time
C Lightlike
D Spacelike
Length contraction occurs only
A Perpendicular to motion
B Parallel to motion
C Independently of direction
D In accelerated frames only
Relativistic Doppler shift includes
A Classical Doppler + time dilation
B Only shift due to motion
C Only time dilation
D Only graviational shift
If a source approaches an observer, the wavelength
A Increases
B Decreases
C Remains same
D Goes to zero
If v → c, γ →
A 1
B 0
C ∞
D −1
Relativistic kinetic energy can be approximated at small v as
A γmc²
B 12mv2\frac12 mv^221mv2
C mc²
D c²/v
Rest mass is defined in the frame where
A Object moves at speed c
B Object is at rest
C Object accelerates
D Object is massless
For a massive particle, energy is minimized when
A v = c
B v = 0
C v = c/2
D v < 0
Lorentz contraction is symmetric in SR?
A Yes, each sees the other’s lengths contracted
B No, only one contracts
C Neither sees contraction
D Contraction is irrelevant
In relativistic dynamics, force parallel to velocity gives
A Classical acceleration a = F/m
B Reduced acceleration due to γ³ factor
C Infinite acceleration
D Zero acceleration
In a perfectly elastic relativistic collision, what is conserved?
A Only momentum
B Only energy
C 4-momentum
D Mass only
In relativistic aberration, light from a star appears
A Shifted backward
B Shifted forward into direction of motion
C Unchanged
D Split into two beams
In SR, simultaneity breakdown implies that
A Causality is violated
B Time ordering of spacelike events can differ between observers
C No time exists
D Clocks cannot be synchronized
The transverse Doppler effect is purely caused by
A Relative motion along line of sight
B Time dilation
C Gravitational field
D Temperature
For massless particles, proper time between any two events on their worldline is
A Maximum
B Negative
C Zero
D Infinite
According to relativity, mass
A Increases with velocity (old view)
B Is invariant (modern), momentum changes
C Depends on temperature
D Depends on chemical potential
In relativistic thermodynamics, temperature transformation is often treated using
A Lorentz invariance only
B Einstein–Planck formulation
C Newtonian formulas
D No transformation needed
Photon energy transforms under Doppler shift as
A E → E
B E → E√((1+β)/(1−β))
C E → 2E
D E → E/γ
Invariance of charge means
A Total charge changes with frame
B Charge of particle is same in all inertial frames
C Charge dilates
D Charge contracts
Pressure of a relativistic ideal gas depends on
A Only momentum
B Energy density
C Temperature only
D Speed only
For a photon gas, equation of state is
A P = U/V
B P = U/(3V)
C P = 0
D P = 2U/V
In a Fermi gas at low temperature, entropy
A Is large
B Is nearly zero
C Diverges
D Oscillates
Relativistic beaming causes radiation to
A Spread uniformly
B Concentrate in forward direction
C Go backward
D Vanish
Speed of a particle cannot reach c because
A Air resistance
B Gravity
C Requires infinite energy
D Electron charge
Lorentz transformation matrix preserves
A Dot product of vectors
B Minkowski metric
C Volumes only
D Energy only
The Compton wavelength λC=h/(mc)\lambda_C = h/(mc)λC=h/(mc) is
A Zero for electrons
B Characteristic quantum-relativistic scale for particles
C Only for photons
D Always large
Partition function determines
A Only pressure
B All thermodynamic properties (via derivatives)
C Only entropy
D Nothing physical
Grand partition function accounts for
A Only T
B T, V, μ
C T and μ but not V
D None of these
A negative chemical potential in BE statistics ensures
A Unlimited occupation
B Physical occupation numbers (no divergence except at condensation threshold)
C No particles
D Fermi energy shift