Physical Chemistry

GATE Chemistry (CY) — Statistical Thermodynamics previous year questions

16 questions · 2005 · all with verified answer · last checked 2026-11-10

Q1 · 2005-2021 · 2 marks

Column-I Column - II P. Many electron wave function I. Adiabatic demagnetization Q. Low temperature II. Slater determinant R. Mean speed III. Partition function S. Molecular ensemble IV. maxwellian distribution V. LCAO - MO VI. Photoejection Codes:

(a) P - IV, Q - I, R - VI, S - III
(b) P - II, Q - I, R - IV, S - III
(c) P - II, Q - V, R - VI, S - IV
(d) P - VI, Q - IV, R - III, S - II

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Answer: (b)

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Q2 · 2005-2021 · 2 marks

The vibrational partition function for a molecule with fundamental frequency \nu is given by

(a) \exp\left(-\frac{\hbar\nu}{k_{\mathrm B}T}\right)
(b) \left[1-\exp\left(-\frac{\hbar\nu}{k_{\mathrm B}T}\right)\right]^{-1}
(c) \exp\left(-\frac{\hbar\nu}{k_{\mathrm B}T}\right)\left[1-\exp-\left(\frac{\hbar\nu}{k_{\mathrm B}T}\right)\right]^{-1}
(d) \exp\left(-\frac{\hbar\nu}{2k_{\mathrm B}T}\right)\left[1-\exp-\left(\frac{\hbar\nu}{k_{\mathrm B}T}\right)\right]^{-1}

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Answer: (d)

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Q3 · 2005-2021 · 2 marks

Given that the mean speed of \mathrm{H_2} is 1.78\ \mathrm{km\,s^{-1}}, the mean speed of \mathrm{D_2} will be

(a) 1.26\ \mathrm{km\,s^{-1}}
(b) 2.52\ \mathrm{km\,s^{-1}}
(c) 5.04\ \mathrm{km\,s^{-1}}
(d) 3.17\ \mathrm{km\,s^{-1}}

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Answer: (a)

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Q4 · 2005-2021 · 2 marks

As the temperature tends to infinity, the partition function for a two-level system is

(a) 0
(b) 1
(c) 2
(d) infinity

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Answer: (c)

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Q5 · 2005-2021 · 2 marks

Assuming \mathrm{H_2} and HD molecules having equal lengths, the ratio of the rotational partition functions of these molecules, at temperature above 100 K is

(a) 3/8
(b) 3/4
(c) 1/2
(d) 2/3

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Answer: (a)

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Q6 · 2005-2021 · 2 marks

At T = 300 K, the thermal energy (k_BT) in \mathrm{cm^{-1}} is approximately

(a) 20000
(b) 8000
(c) 5000
(d) 200

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Answer: (d)

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Q7 · 2005-2021 · 2 marks

The total number of ways in which two nonidentical spin–\frac{1}{2} particles can be oriented relative to a constant magnetic field is:

(a) 1
(b) 2
(c) 3
(d) 4

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Answer: (d)

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Q8 · 2005-2021 · 2 marks

A box of volume V contains one mole of an ideal gas. The probability that all N particles will be found occupying one half of the volume leaving the other half empty is

(a) 1/2
(b) 2/N
(c) (1/2)^N
(d) (1/2)^{6N}

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Answer: (c)

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Q9 · 2005-2021 · 2 marks

A certain molecule can be treated as having only a doubly degenerate state lying at 360\ \mathrm{cm}^{-1} above the nondegenerate ground state. The approximate temperature (K) at which 15% of the molecule will be in the upper state is

(a) 500
(b) 150
(c) 200
(d) 300

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Answer: (c)

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Q10 · 2005-2021 · 2 marks

The ratio of molecules distributed between two states is 9.22 \times 10^{6} at 300K. the difference in energy (in \mathrm{kJ\,mol^{-1}}) of the two states is ________

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Answer: 39.98

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Q11 · 2005-2021 · 2 marks

For an ideal gas with molar mass M, the molar translational entropy at a given temperature is proportional to

(a) M^{3/2}
(b) M^{1/2}
(c) e^{M}
(d) \ln(M)

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Answer: (b)

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Q12 · 2005-2021 · 2 marks

The rotational partition function of a diatomic molecule with energy levels corresponding to J = 0, 1, is (where, \varepsilon is a constant)

(a) 1 + e^{-2\varepsilon}
(b) 1 + 3e^{-2\varepsilon}
(c) 1 + e^{-3\varepsilon}
(d) 1 + 3e^{-3\varepsilon}

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Answer: (b)

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Q13 · 2005-2021 · 2 marks

Consider a two-state system at thermal equilibrium with equal degeneracy where the excited state is higher in energy than the ground state by 0.1 eV. The ratio of the population of the excited state to that of the ground state, at a temperature for which k_B T = 0.05 eV, is ____

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Answer: 0.14

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Q14 · 2005-2021 · 2 marks

Consider N particles at temperature T, pressure P, Volume V and chemical potential \mu having energy E. The parameters that are kept constant for a canonical ensemble are

(a) N, V, T
(b) N, V, E
(c) N, P, T
(d) \mu, V, T

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Answer: (a)

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Q15 · 2005-2021 · 2 marks

Consider a two-state system at thermal equilibrium having energies 0 and 2 \mathrm{k}_{\mathrm{B}} \mathrm{T} for which the degenracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is ____ . (Round off to two decimal places) ( \mathrm{k}_{\mathrm{B}} is the Boltzmann constant)

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Answer: 1.27

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Q16 · 2005-2021 · 2 marks

Consider a system of three identical and distinguishable non-interacting particles and three available nondegenerate single particle energy levels having energies 0, \varepsilon and 2 \varepsilon. The system is in contact with a heat bath of temperature TK. A total energy of 2 \varepsilon is shared by these three particles. The number of ways the particles can be distributed is ____ STATISTICAL THERMO ANSWERS KEY

1.	(b)	2.	(d)	3.	(a)	4.	(c)	5.	(a)	6.	(a)	7.	(d)
8.	(d)	9.	(c)	10.	(c)	11.	(a)	12.	(39.98)	13.	(b)	14.	(b)
15.	(0.14)	16.	(a)	17.	(1.27)	18.	(6)

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Answer: 6

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