In Maxwell–Boltzmann statistics, particles are treated as
A Indistinguishable
B Fermions only
C Bosons only
D Distinguishable classical particles
In MB statistics, occupation numbers of energy states are
A Large and allowed to be negative
B Unrestricted and small compared to 1
C Restricted to 0 or 1
D Restricted to even numbers only
Maxwell–Boltzmann distribution is most accurate when
A nλ3≪1n \lambda^3 \ll 1nλ3≪1
B nλ3≫1n \lambda^3 \gg 1nλ3≫1
C Very low temperatures
D Particles are bosons
Classical limit: low density or high temperature.
Fermi–Dirac distribution reduces to MB distribution when
A T → 0
B e^{(E−μ)/kT} ≫ 1
C e^{(E−μ)/kT} ≪ 1
D μ → 0
High energy compared to chemical potential → classical limit.
Fermi energy of metal depends on
A Temperature
B Density of electrons
C External field
D Pressure only
At T = 0 K, the occupation probability of a state with E < EF is
A 0
B 0.5
C 1
D Undefined
Bose–Einstein condensation occurs when
A High temperature
B Low temperature and high density
C Very high pressure
D Very high velocity
In Bose–Einstein condensation, a significant fraction of bosons occupy
A Highest energy state
B Random states
C Single lowest energy state
D Forbidden region
Blackbody radiation follows
A MB statistics
B BE statistics
C FD statistics
D Poisson statistics
The Sackur–Tetrode entropy applies to
A Quantum ideal gas only
B Classical monatomic ideal gas
C Fermi gas
D Photon gas
In thermodynamic equilibrium, entropy is
A Minimum
B Maximum
C Constant at all temperatures
D Zero always
Irreversibility occurs due to
A Limited energy
B Spontaneous evolution to macrostates with higher probability
C Mathematical errors
D Microscopic irreversibility
The Helmholtz free energy decreases for
A Constant T and V (spontaneous process)
B Constant P and T
C Constant S and V
D Constant μ and T
The Gibbs free energy decreases for
A Constant T and P
B Constant V only
C Constant S only
D Constant μ only
Enthalpy is defined as
A H = TS + PV
B H = U + PV
C H = T/U
D H = U – TS
Maxwell relation from Gibbs free energy G(T,P) includes
A (∂S∂P)T=−(∂V∂T)P\left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P(∂P∂S)T=−(∂T∂V)P
B (∂U∂S)V=T\left(\frac{\partial U}{\partial S}\right)_V = T(∂S∂U)V=T
C (∂H∂T)P=CP\left(\frac{\partial H}{\partial T}\right)_P = C_P(∂T∂H)P=CP
D P=−(∂F∂V)TP = -\left(\frac{\partial F}{\partial V}\right)_TP=−(∂V∂F)T
Chemical potential μ is defined as
A μ=(∂U∂N)S,V\mu = \left( \frac{\partial U}{\partial N} \right)_{S,V}μ=(∂N∂U)S,V
B Depends only on temperature
C Always constant
D Zero in ideal gas
Canonical ensemble keeps which quantity fixed?
A N, V, T
B N, P, T
C μ, V, T
D E, V, N
Microcanonical ensemble keeps which quantities fixed?
A T, V, μ
B E, V, N
C T, P, N
D E, P, T
Relativistic time dilation tells that a moving clock
A Runs faster
B Runs slower
C Stops
D Accumulates negative time
If an astronaut ages 1 year during a high-speed trip and people on Earth age 5 years, the astronaut experienced
A Time contraction
B Time dilation (proper time smaller)
C Length dilation
D No relativistic effect
Lorentz factor γ depends on
A Acceleration only
B Velocity relative to light speed
C Mass only
D Temperature
A rod moving at speed v parallel to its length appears
A Longer
B Shorter
C Same length
D Bent
Proper length is
A Length measured in moving frame
B Shortest measurable length
C Length measured in object’s rest frame
D Variable due to heat
If mass m moves with relativistic speed, its momentum is
A mv
B γmv\gamma mvγmv
C mv2m v^2mv2
D mc2m c^2mc2
As v → c, relativistic momentum
A Decreases
B Remains constant
C Increases without bound
D Changes sign
Relativistic kinetic energy is
A K=mc2K = mc^2K=mc2
B K=(γ−1)mc2K = (\gamma – 1)mc^2K=(γ−1)mc2
C K=12mv2K = \frac{1}{2}mv^2K=21mv2
D K=γmc2K = \gamma mc^2K=γmc2
Einstein’s mass–energy equivalence means
A Energy is independent of mass
B Mass and energy are interchangeable
C Energy cannot be converted
D Mass is always constant
Photon momentum arises because
A Photons have rest mass
B Electromagnetic waves carry momentum p=h/λp = h/\lambdap=h/λ
C Photons are negative energy carriers
D Light slows down in vacuum
Lorentz transformations preserve which physical quantity?
A Energy only
B Momentum only
C Spacetime interval
D Temperature
The speed of light is invariant because
A Photons accelerate
B It is postulated and experimentally verified
C Air blocks deviation
D Mirrors reflect perfectly
Michelson–Morley experiment used
A Two perpendicular light paths (interferometer)
B Gamma rays
C Mechanical clocks
D Electrons
A null result in Michelson–Morley means
A Earth is stationary
B No difference in light speed in different directions
C Light does not exist
D Newtonian mechanics is wrong
In SR, simultaneity depends on
A Position only
B Reference frame
C Temperature
D Mass of observer
If two events have spacelike separation, they cannot
A Influence each other causally
B Occur
C Be observed
D Occur simultaneously
For timelike intervals, all observers agree on
A Time ordering of events
B Spatial ordering
C That events are simultaneous
D Reversal of events
Proper time between two events is
A Maximal for light
B Zero for photons
C Non-zero for massive particles
D Variable depending on temperature
In relativistic Doppler effect, receding source shows
A Blueshift
B Redshift
C No shift
D Stopped oscillation
A muon traveling near light speed appears to live longer because
A Its mass decreases
B Time dilation increases lifetime in lab frame
C Its decay stops
D It stores energy
In relativistic energy–momentum relation E2=p2c2+m2c4E^2 = p^2c^2 + m^2c^4E2=p2c2+m2c4, for large p the energy behaves as
A Linear in p
B Quadratic in p
C Zero
D Constant
Momentum of a photon with wavelength λ is
A λ/h
B h/λ
C hc/λ
D 1/λ²
Relativistic mass concept (m = γm₀) is
A Fundamental
B Replaced in modern physics by invariant rest mass m₀
C Increasingly used
D Equivalent to charge
A particle with zero rest mass must
A Travel slower than light
B Travel at speed of light
C Be accelerated to rest
D Not exist
For a traveling observer, the distance to Earth appears
A Longer
B Contracted
C Same
D Infinite
Total energy of particle includes
A Only kinetic
B Only potential
C Rest + kinetic
D Only thermal
Relativistic kinetic energy for small speeds reduces to
A 12mv2\frac{1}{2}mv^221mv2
B mc2mc^2mc2
C mv2mv^2mv2
D Zero
Lorentz transformation mixes
A x and y
B t and x
C mass and temperature
D μ and N
Speed of light constancy leads to
A Time contraction
B Time dilation and length contraction
C Mass negation
D Faster-than-light motion
Energy of a photon emitted by a moving source depends on
A Doppler shift
B Pressure
C Gravity only
D Temperature only
Inertia of a body increases with speed because
A Mass increases
B Relativistic momentum increases
C Friction increases
D Potential energy increases