Thermodynamics and Statistical Physics MCQs Question and Answer in Engineering Physics

1.
A system has two energy levels with energies E and 2E. The lower level is four-fold degenerate while the upper level is doubly degenerate. If there are N non-interacting classical particles in the system, which is in thermodynamic equilibrium at temperature T, the fraction of particles in the upper level is

A. $$\frac{1}{{1 + {e^{ - \varepsilon /{k_B}T}}}}$$

B. $$\frac{1}{{1 + 2{e^{\varepsilon /{k_B}T}}}}$$

C. $$\frac{1}{{2{e^{\varepsilon /{k_B}T}} + 4{e^{2\varepsilon /{k_B}T}}}}$$

D. $$\frac{1}{{2{e^{\varepsilon /{k_B}T}} - 4{e^{2\varepsilon /{k_B}T}}}}$$

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2.
A system of non-interacting Fermi particles with Fermi energy E_F has the density of states proportional to √E, where E is the energy of a particle. The average energy per particle at temperature T = 0 is

A. $$\frac{1}{6}{E_F}$$

B. $$\frac{1}{5}{E_F}$$

C. $$\frac{2}{5}{E_F}$$

D. $$\frac{3}{5}{E_F}$$

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3.
A piston containing an ideal gas is originally in the state X (see figure). The gas is taken through a thermal cycle X → Y → X as shown

The work done by the gas is positive, if the direction of the thermal cycle is

A. clockwise

B. counter-clockwise

C. neither clockwise nor counter-clockwise

D. clockwise from X → Y and counter-clockwise from Y → X

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4.
A photon gas is at thermal equilibrium at temperature T. The mean number of photons in an energy state $$\varepsilon = h\omega $$ is

A. $$\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right) + 1$$

B. $$\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right) - 1$$

C. $${\left[ {\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right) + 1} \right]^{ - 1}}$$

D. $${\left[ {\exp \left( {\frac{{\hbar \omega }}{{{k_B}T}}} \right) - 1} \right]^{ - 1}}$$

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5.
In a classical micro-canonical ensemble for a system of N non-interacting particles, the fundamental volume in phase space which is regarded as equivalent to one micro-state is
(where, h is the Planck's constant.)

A. h^3N

B. h^2N

C. h^N

D. h

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6.
In the region of co-existence of a liquid and vapour phases of a material

A. C_p and C_V are both infinite

B. C_V and $$\beta \left[ { = \frac{1}{V}{{\left( {\frac{{\partial V}}{{\partial T}}} \right)}_p}} \right]$$ are both infinite

C. C_V and $$K\left[ { = - \frac{1}{V}{{\left( {\frac{{\partial V}}{{\partial p}}} \right)}_T}} \right]$$ are both infinite

D. C_p, β and K are all infinite

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7.
For a Fermi gas of N particles in three-dimensions at T = 0 K, the Fermi energy E_F is proportional to

A. $${N^{\frac{2}{3}}}$$

B. $${N^{\frac{3}{2}}}$$

C. $${N^3}$$

D. $${N^2}$$

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8.
The partition function of two Bose particles, each of which can occupy any of the two energy levels 0 and $$\varepsilon $$ is

A. $$1 + {e^{\frac{{ - 2\varepsilon }}{{kT}}}} + 2{e^{\frac{{ - \varepsilon }}{{kT}}}}$$

B. $$1 + {e^{\frac{{ - 2\varepsilon }}{{kT}}}} + {e^{\frac{{ - \varepsilon }}{{kT}}}}$$

C. $$2 + {e^{\frac{{ - 2\varepsilon }}{{kT}}}} + {e^{\frac{{ - \varepsilon }}{{kT}}}}$$

D. $${e^{\frac{{ - 2\varepsilon }}{{kT}}}} + 2{e^{\frac{{ - \varepsilon }}{{kT}}}}$$

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9.
It is necessary to apply quantum statistics to a system of particles, if

A. there is substantial overlap between the wave functions of the particles

B. the mean free path of the particles is comparable to the inter-particle separation

C. the particles have identical mass and charge

D. the particles are interacting

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10.
Consider the Fermi-Dirac distribution function f(E) at room temperature (300 K), where E refers tb energy. If E_F is the Fermi energy, which of the following is true?

A. f(E) is a step function

B. f(E_F) has a value of $$\frac{1}{2}$$

C. States with E < E_F are filled completely

D. f(E) is large and tends to infinity as E decreases much below E_F

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Thermodynamics and Statistical Physics MCQs Question and Answer in Engineering Physics

Answer & Solution

2. A system of non-interacting Fermi particles with Fermi energy EF has the density of states proportional to √E, where E is the energy of a particle. The average energy per particle at temperature T = 0 is

Answer & Solution

3. A piston containing an ideal gas is originally in the state X (see figure). The gas is taken through a thermal cycle X → Y → X as shown The work done by the gas is positive, if the direction of the thermal cycle is

Answer & Solution

4. A photon gas is at thermal equilibrium at temperature T. The mean number of photons in an energy state $$\varepsilon = h\omega $$ is

Answer & Solution

5. In a classical micro-canonical ensemble for a system of N non-interacting particles, the fundamental volume in phase space which is regarded as equivalent to one micro-state is (where, h is the Planck's constant.)

Answer & Solution

6. In the region of co-existence of a liquid and vapour phases of a material

Answer & Solution

7. For a Fermi gas of N particles in three-dimensions at T = 0 K, the Fermi energy EF is proportional to

Answer & Solution

8. The partition function of two Bose particles, each of which can occupy any of the two energy levels 0 and $$\varepsilon $$ is

Answer & Solution

9. It is necessary to apply quantum statistics to a system of particles, if

Answer & Solution

10. Consider the Fermi-Dirac distribution function f(E) at room temperature (300 K), where E refers tb energy. If EF is the Fermi energy, which of the following is true?

Answer & Solution

2.
A system of non-interacting Fermi particles with Fermi energy E_F has the density of states proportional to √E, where E is the energy of a particle. The average energy per particle at temperature T = 0 is

3.
A piston containing an ideal gas is originally in the state X (see figure). The gas is taken through a thermal cycle X → Y → X as shown

The work done by the gas is positive, if the direction of the thermal cycle is

4.
A photon gas is at thermal equilibrium at temperature T. The mean number of photons in an energy state $$\varepsilon = h\omega $$ is

5.
In a classical micro-canonical ensemble for a system of N non-interacting particles, the fundamental volume in phase space which is regarded as equivalent to one micro-state is
(where, h is the Planck's constant.)

6.
In the region of co-existence of a liquid and vapour phases of a material

7.
For a Fermi gas of N particles in three-dimensions at T = 0 K, the Fermi energy E_F is proportional to

8.
The partition function of two Bose particles, each of which can occupy any of the two energy levels 0 and $$\varepsilon $$ is

9.
It is necessary to apply quantum statistics to a system of particles, if

10.
Consider the Fermi-Dirac distribution function f(E) at room temperature (300 K), where E refers tb energy. If E_F is the Fermi energy, which of the following is true?