GATE CY concept:partition-functions PYQs & Answers

Questions 1–7 of 7. Imported answers require independent review unless marked reviewed.

If the translation partition function for H₂ confined in a 1 L vessel at 300 K is

, then the value of y is ______ (rounded off to one decimal place).

(Given: Atomic mass (in amu): H = 1.008; 1 amu = 1.661 × 10⁻²⁷ kg; h = 6.626 × 10⁻³⁴ J s; k = 1.381 × 10⁻²³ J K⁻¹)

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The translational, vibrational, and rotational molecular partition functions for a system containing ideal diatomic gas molecules in the canonical ensemble (N, V, T) are written as

, and

, respectively. The option that correctly defines their thermodynamic variable(s) dependency is

Your answerChoose one option.

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An approximate partition function

of a gas is given below.

The equation of state(s) for this gas is/are

[Note:

is a parameter independent of volume.]

Your answerSelect all correct options. You can choose more than one.

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and

are the molecular and molar translational partition functions of X₂, respectively, then

(N is the Avogadro number)

Your answerChoose one option.

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For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (V), is the

Your answerChoose one option.

vibrational partition function

rotational partition function

electronic partition function

translational partition function

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Consider a two-state system at thermal equilibrium having energies 0 and 2kᵦT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is __________. (Round off to two decimal places) (kᵦ is the Boltzmann constant)

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At temperature T, the canonical partition function of a harmonic oscillator with fundamental frequency (ν) is given by

For

, the probability of finding the harmonic oscillator in its ground vibrational state is ________. (Up to two decimal places)

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GATE CY concept:partition-functions PYQs

How to practice concept:partition-functions

Question 62

Question 20

Question 47

Question 47

Question 29

Question 22

Question 46