For a photon gas, internal energy U is proportional to
A T
B T³
C T⁴
D 1/T
Blackbody: U∝T4U \propto T^4U∝T4.
Entropy of photon gas varies as
A T
B T²
C T³
D T⁴
Entropy density ∝ T³.
In BE statistics, occupation number diverges when
A E = μ
B E > μ
C μ → -∞
D T → ∞
A degenerate Fermi gas at T=0 has
A Random distribution of particles
B All states filled up to EF
C No occupied states
D Infinite temperature
Equation of state of classical ideal gas arises from
A Fermi–Dirac statistics
B Maxwell–Boltzmann statistics
C Bose–Einstein statistics
D Quantum entanglement
For fermions, the Pauli exclusion principle enforces
A Multiple occupancy
B At most 1 particle per quantum state
C Infinite occupancy
D No occupancy
Degeneracy pressure in white dwarfs is due to
A Thermal motion
B Electron Fermi pressure
C Nuclear reactions
D Ion collisions
Partition function Z is crucial because
A It determines only pressure
B It determines all thermodynamic averages
C It has no physical meaning
D It only defines entropy
Helmholtz free energy determines equilibrium for
A Constant T, V
B Constant T, P
C Constant S, V
D Constant μ
Gibbs free energy determines equilibrium for
A Constant P, T
B Constant S
C Constant V
D Constant μ
If dG < 0 at constant T,P, process is
A Non-spontaneous
B Spontaneous
C Static
D Forbidden
Grand potential Ω = U − TS − μN is natural for
A fixed T, V, μ
B fixed T, P
C fixed S, V
D fixed T, S
Entropy increases because
A Microstates become less likely
B Number of accessible microstates increases
C Temperature decreases
D Pressure decreases
Heat death of the universe concept is associated with
A Minimum entropy
B Maximum entropy
C Zero energy
D Negative entropy
Lorentz transformation keeps which quantity invariant?
A Time
B Length
C Speed of light and spacetime interval
D Mass
Proper time is greatest for
A Light
B Any object moving at high speed
C Object at rest between two events
D No object
For light, the proper time between emission and detection is
A Zero
B Positive
C Negative
D Infinite
Relativistic total energy E of a particle is
A pc
B mc²
C γmc2\gamma mc^2γmc2
D 12mv2\frac{1}{2}mv^221mv2
For massive particle, minimizing total energy occurs when
A v = c
B v = 0
C v = c/2
D v increases
If particle speed doubles (relativistic regime), momentum increases
A Linearly
B Less than linearly
C Faster than linearly
D Decreases
Energy–momentum relation reduces to classical KE when
A v ≪ c
B v ≈ c
C m = 0
D p = 0
For a photon:
A E = 0
B E = pc
C E = mc²
D E = γmc²
Relativistic Doppler shift formula includes both classical Doppler and
A Length contraction
B Time dilation
C Gravitational shift only
D Aberration
When source recedes at relativistic speed, wavelength
A Decreases
B Increases (redshift)
C Constant
D Doubles exactly
Relativistic aberration causes incoming light to
A Spread uniformly
B Compress into forward direction
C Shift sideways only
D Disappear
4-velocity of a particle has magnitude
A 0
B c
C v
D Undefined
Magnitude of 4-velocity is always c for massive particles.
4-momentum Pμ=(E/c,p)P^\mu = (E/c, \mathbf{p})Pμ=(E/c,p) has invariant
A E + p
B E − p
C PμPμ=m2c2P^\mu P_\mu = m^2 c^2PμPμ=m2c2
D EPEPEP constant
Relativistic mass is replaced by
A Variable mass
B Invariant rest mass and relativistic momentum
C No mass
D Imaginary number
For ultrarelativistic particles (E ≫ mc²), energy approximates
A mc²
B pc
C p²/2m
D 0
Causality is preserved in SR because
A Faster-than-light communication forbidden
B Time dilation
C Length contraction
D Energy conservation
In SR, two timelike-separated events:
A Cannot influence each other
B Must occur at same time
C Have invariant time ordering
D Can reverse order
Two spacelike-separated events:
A Can be causally connected
B Cannot influence each other
C Have fixed time ordering
D Must be simultaneous
Energy of particle at rest is
A Zero
B mc²
C pc
D m/p
A particle requires infinite energy to reach
A 0
B c
C c/2
D 0.9c
Thermal equilibrium in statistical mechanics requires
A Same momentum
B Equal temperatures
C Equal energies
D Equal entropies
Pressure in ideal gas arises from
A Quantum fluctuations
B Collisions of particles with container walls
C Radiation
D Entanglement
Density of states in 3D varies as
A √E
B E
C E²
D 1/E
White dwarf stability is provided by
A Nuclear fusion
B Electron degeneracy pressure
C Iron core
D Gravity
BE condensation temperature decreases as
A Density decreases
B Density increases
C Temperature increases
D Pressure increases
FD distribution prevents
A Thermal motion
B More than one fermion from occupying same state
C Photon creation
D Random distribution
If a gas is quantum degenerate, then
A nλ³ ≪ 1
B nλ³ ≫ 1
C nλ³ = 0
D No dependence on λ
Spacetime diagram representation uses
A Time as vertical axis and position as horizontal
B Temperature and mass
C Charge and energy
D Probability and entropy
Light cone divides events into
A Large and small
B Timelike, spacelike, lightlike
C Present and future only
D Physical and nonphysical
If s² < 0 for an interval, it is
A Timelike
B Spacelike
C Lightlike
D Undefined
If s² > 0 for an interval, it is
A Timelike
B Spacelike
C Lightlike
D Imaginary
Relativistic energy of electron with v ≈ c remains finite because
A γ stays small
B m becomes zero
C γ grows but finite energy input (< ∞ for v < c)
D Momentum decreases
Maxwell relations arise due to
A Nonlinearity
B Equality of mixed second derivatives of thermodynamic potentials
C Random processes
D Entropy fluctuations only
A reversible process is characterized by
A ΔS > 0
B ΔS = 0
C ΔS < 0
D No entropy
Heat capacity at constant volume is given by
A CV=(∂U/∂T)VC_V = (\partial U/\partial T)_VCV=(∂U/∂T)V
B CV=(∂H/∂T)PC_V = (\partial H/\partial T)_PCV=(∂H/∂T)P
C CV=PV/TC_V = PV/TCV=PV/T
D CV=−T(∂2F/∂T2)C_V = -T(\partial^2 F/\partial T^2)CV=−T(∂2F/∂T2) only
The entropy of an isolated system never decreases because
A Energy is lost
B Motion stops
C Evolves toward the macrostate with highest probability (2nd Law)
D Statistical fluctuations vanish