Partition Functions MCQs with Answers

adminApril 12, 2024

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Welcome to the Partition Functions MCQs with Answers. In this post, we have shared Partition Functions Online Test for different competitive exams. Find practice Partition Functions Practice Questions with answers in Physics Tests exams here. Each question offers a chance to enhance your knowledge regarding Partition Functions.

Partition Functions Online Quiz

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Test Name: Partition Functions MCQ Quiz Practice
Type: Quiz Test
Total Questions: 40
Total Marks: 40
Time: 40 minutes

Note: Answer of the questions will change randomly each time you start the test. Practice each quiz test at least 3 times if you want to secure High Marks. Once you are finished, click the View Results button. If any answer looks wrong to you in Quizzes. simply click on question and comment below that question. so that we can update the answer in the quiz section.

Partition Functions

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1 / 40

What is the partition function for an ideal gas in a one-dimensional box?

B) 𝑍=𝐿𝑁𝜆3Z=Nλ3L

C) 𝑍=𝐿𝑁𝜆2Z=Nλ2L

A) 𝑍=𝐿𝑁𝜆Z=NλL

2 / 40

What is the partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta when 𝑞≪𝑁q≪N?

B) 𝑍=𝑞𝑁Z=qN

A) 𝑍=𝑁𝑞𝑞!Z=q!Nq

C) 𝑍=(𝑞+𝑁−1)!𝑞!(𝑁−1)!Z=q!(N−1)!(q+N−1)!

3 / 40

Which of the following is a property of the canonical partition function?

C) It depends on the number of particles

B) It is a function of temperature only

A) It is independent of temperature

4 / 40

What is the partition function for a monoatomic ideal gas in a one-dimensional box?

A) 𝑍=𝐿𝑁𝜆Z=NλL

C) 𝑍=𝐿𝑁𝜆2Z=Nλ2L

B) 𝑍=𝐿𝑁𝜆3Z=Nλ3L

5 / 40

Which of the following is a correct expression for the canonical partition function of a system in statistical mechanics?

C) 𝑍=1𝑁∑𝑖𝑒−𝛽𝐸𝑖Z=N1∑ie−βEi

B) 𝑍=1𝑁!∑𝑖𝑒−𝛽𝐸𝑖Z=N!1∑ie−βEi

A) 𝑍=∑𝑖𝑒−𝛽𝐸𝑖Z=∑ie−βEi

6 / 40

The partition function for a system of distinguishable particles is given by

C) 𝑍=∑𝑖𝑒−𝛽𝐸𝑖Z=∑ie−βEi

A) 𝑍=1𝑁!∑𝑖𝑒−𝛽𝐸𝑖Z=N!1∑ie−βEi

B) 𝑍=1𝑁∑𝑖𝑒−𝛽𝐸𝑖Z=N1∑ie−βEi

7 / 40

The partition function for a monatomic ideal gas at high temperatures approaches what value?

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆Z=NλV

C) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

8 / 40

The partition function of an ideal gas at constant temperature and volume is proportional to

B) The volume

A) The temperature

C) The number of particles

9 / 40

The partition function for a system with indistinguishable particles is calculated by

C) Using the Stirling approximation

A) Considering the quantum nature of particles

B) Summing over all possible microstates

10 / 40

What is the partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta when 𝑞≫𝑁q≫N?

B) 𝑍=𝑞𝑁Z=qN

C) 𝑍=(𝑞+𝑁−1)!𝑞!(𝑁−1)!Z=q!(N−1)!(q+N−1)!

A) 𝑍=𝑁𝑞𝑞!Z=q!Nq

11 / 40

At low temperatures, the partition function for a diatomic molecule approaches what value?

A) 𝑍=𝑉𝑁Z=NV

C) 𝑍=0Z=0

B) 𝑍=1Z=1

12 / 40

Which of the following statements about the partition function is correct?

B) It depends only on temperature

C) It is independent of the number of particles

A) It accounts for the quantization of energy levels

13 / 40

What is the partition function for a monatomic ideal gas?

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

C) 𝑍=𝑉𝑁𝜆Z=NλV

14 / 40

What is the partition function for a monatomic ideal gas in a two-dimensional box?

B) 𝑍=𝐴𝑁𝜆2Z=Nλ2A

C) 𝑍=𝐴𝑁𝜆3Z=Nλ3A

A) 𝑍=𝐴𝑁𝜆Z=NλA

15 / 40

What is the partition function for a diatomic molecule at low temperatures?

B) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

C) 𝑍=𝑉𝑁Z=NV

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

16 / 40

The partition function of an ideal gas at constant temperature and volume is proportional to

C) The number of particles

B) The volume

A) The temperature

17 / 40

The partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta when 𝑞=𝑁q=N?

B) 𝑍=𝑞𝑁Z=qN

C) 𝑍=(𝑞+𝑁−1)!𝑞!(𝑁−1)!Z=q!(N−1)!(q+N−1)!

A) 𝑍=𝑁𝑞𝑞!Z=q!Nq

18 / 40

What is the partition function for a monoatomic ideal gas in a two-dimensional box?

C) 𝑍=𝐴𝑁𝜆3Z=Nλ3A

A) 𝑍=𝐴𝑁𝜆Z=NλA

B) 𝑍=𝐴𝑁𝜆2Z=Nλ2A

19 / 40

At what temperature does the partition function of an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta reach its maximum value?

A) At all temperatures

B) At 𝑇=0T=0

C) At 𝑇=∞T=∞

20 / 40

What is the partition function for a monoatomic ideal gas in a three-dimensional box?

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆Z=NλV

C) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

21 / 40

The partition function for a monatomic ideal gas at low temperatures approaches what value?

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆Z=NλV

C) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

22 / 40

The partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta is maximum when

C) 𝑞=𝑁2q=2N

A) 𝑞=0q=0

B) 𝑞=𝑁q=N

23 / 40

Which of the following is true about the partition function of an ideal gas?

A) It decreases with increasing temperature

B) It increases with increasing volume

C) It depends on the mass of the gas particles

24 / 40

The partition function for an ideal gas is dependent on which of the following?

A) Temperature and volume

B) Pressure and temperature

C) Volume and pressure

25 / 40

At high temperatures, the partition function for a diatomic molecule approaches what value?

C) 𝑍=𝑉𝑁Z=NV

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

26 / 40

The canonical partition function for an ideal gas at constant temperature and volume is

C) 𝑍=∑𝑖𝑒−𝛽𝐸𝑖Z=∑ie−βEi

A) 𝑍=1𝑁!∑𝑖𝑒−𝛽𝐸𝑖Z=N!1∑ie−βEi

B) 𝑍=1𝑁∑𝑖𝑒−𝛽𝐸𝑖Z=N1∑ie−βEi

27 / 40

Which of the following is NOT a property of the partition function?

B) It is a function of temperature only

C) It depends on the system's quantum states

A) It gives information about the energy distribution

28 / 40

What is the partition function for a monatomic ideal gas in a three-dimensional box?

B) 𝑍=𝑉𝑁𝜆Z=NλV

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

C) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

29 / 40

Which of the following is a consequence of the Boltzmann distribution?

C) It predicts the entropy of a system

A) It predicts the probability of finding a system in a particular microstate

B) It predicts the total energy of a system

30 / 40

What is the partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta?

A) 𝑍=𝑞𝑁𝑁!Z=N!qN

C) 𝑍=𝑁𝑞Z=Nq

B) 𝑍=𝑞𝑁Z=qN

31 / 40

The partition function for a monatomic ideal gas is NOT affected by

B) The temperature of the system

A) The mass of the gas particles

C) The volume of the container

32 / 40

The partition function for a system of 𝑁N distinguishable particles at fixed temperature is given by

C) 𝑍=1𝑁∑𝑖𝑒−𝛽𝐸𝑖Z=N1∑ie−βEi

A) 𝑍=∑𝑖𝑒−𝛽𝐸𝑖Z=∑ie−βEi

B) 𝑍=1𝑁!∑𝑖𝑒−𝛽𝐸𝑖Z=N!1∑ie−βEi

33 / 40

What is the partition function for a monatomic ideal gas at high temperatures?

C) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆Z=NλV

34 / 40

The partition function for a system with distinguishable particles is calculated how?

C) By considering the indistinguishability of the particles

A) By considering the quantum nature of the particles

B) By summing over all possible microstates

35 / 40

The partition function for an Einstein solid with 𝑁N oscillators and 𝑞q energy quanta can also be written as

A) 𝑍=(𝑞+𝑁−1)!𝑞!(𝑁−1)!Z=q!(N−1)!(q+N−1)!

C) 𝑍=𝑞𝑁Z=qN

B) 𝑍=𝑞𝑁𝑁!Z=N!qN

36 / 40

Which of the following is true regarding the partition function of an ideal gas?

A) It is independent of temperature

B) It depends only on the number of particles

C) It is proportional to the volume

37 / 40

Which of the following is a correct expression for the canonical partition function of a system in statistical mechanics?

A) 𝑍=1𝑁!∑𝑖𝑒−𝛽𝐸𝑖Z=N!1∑ie−βEi

C) 𝑍=∑𝑖𝑒−𝛽𝐸𝑖Z=∑ie−βEi

B) 𝑍=1𝑁∑𝑖𝑒−𝛽𝐸𝑖Z=N1∑ie−βEi

38 / 40

What is the partition function for a diatomic molecule at high temperatures?

B) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

C) 𝑍=𝑉𝑁Z=NV

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

39 / 40

What is the partition function for a diatomic molecule at high temperatures?

A) 𝑍=𝑉𝑁𝜆3Z=Nλ3V

B) 𝑍=𝑉𝑁𝜆2Z=Nλ2V

C) 𝑍=𝑉𝑁Z=NV

40 / 40

The partition function for a system of distinguishable particles is calculated by

A) Considering the indistinguishability of particles

B) Summing over all possible microstates

C) Multiplying the number of particles with Boltzmann constant

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adminApril 12, 2024

0 12 1 minute read