# Statistical Mechanics MCQs with Answers

What branch of physics deals with the behavior of large systems of particles?

a) Quantum mechanics

b) Classical mechanics

c) Statistical mechanics

d) Thermodynamics

**Answer: ** c) Statistical mechanics

What is the fundamental postulate of statistical mechanics?

a) The total energy of a system is conserved

b) The total momentum of a system is conserved

c) The microstates of a system are equally probable

d) The macroscopic properties of a system are determined by its microstates

**Answer: ** d) The macroscopic properties of a system are determined by its microstates

What is entropy in statistical mechanics?

a) The measure of disorder or randomness in a system

b) The total energy of a system

c) The total momentum of a system

d) The temperature of a system

**Answer: ** a) The measure of disorder or randomness in a system

What is the Boltzmann constant denoted by?

a) kB

b) kT

c) kH

d) kE

**Answer: ** a) kB

What is the relation between temperature and average energy in statistical mechanics?

a) Temperature is directly proportional to average energy

b) Temperature is inversely proportional to average energy

c) Temperature is equal to average energy

d) Temperature has no relation to average energy

**Answer: ** b) Temperature is inversely proportional to average energy

What is the probability distribution function that describes the distribution of particles among energy levels in a system?

a) Boltzmann distribution

b) Maxwell-Boltzmann distribution

c) Fermi-Dirac distribution

d) Bose-Einstein distribution

**Answer: ** a) Boltzmann distribution

Which statistical ensemble is used to describe systems with constant energy, volume, and particle number?

a) Microcanonical ensemble

b) Canonical ensemble

c) Grand canonical ensemble

d) Isothermal-isobaric ensemble

**Answer: ** a) Microcanonical ensemble

Which statistical ensemble is used to describe systems in thermal equilibrium with a heat bath?

a) Microcanonical ensemble

b) Canonical ensemble

c) Grand canonical ensemble

d) Isothermal-isobaric ensemble

**Answer: ** b) Canonical ensemble

Which statistical ensemble is used to describe systems in thermal and chemical equilibrium with a heat bath and particle reservoir?

a) Microcanonical ensemble

b) Canonical ensemble

c) Grand canonical ensemble

d) Isothermal-isobaric ensemble

**Answer: ** c) Grand canonical ensemble

Which statistical ensemble is used to describe systems in thermal and mechanical equilibrium with a heat bath and pressure reservoir?

a) Microcanonical ensemble

b) Canonical ensemble

c) Grand canonical ensemble

d) Isothermal-isobaric ensemble

**Answer: ** d) Isothermal-isobaric ensemble

What is the relation between the partition function and the Helmholtz free energy?

a) Partition function is equal to Helmholtz free energy

b) Helmholtz free energy is the logarithm of the partition function

c) Helmholtz free energy is the derivative of the partition function

d) Partition function is the integral of the Helmholtz free energy

**Answer: ** b) Helmholtz free energy is the logarithm of the partition function

What is the average energy of a system in the canonical ensemble?

a) Internal energy

b) Total energy

c) Average kinetic energy

d) Average potential energy

**Answer: ** a) Internal energy

What is the relation between the partition function and the temperature?

a) Partition function is equal to temperature

b) Temperature is the logarithm of the partition function

c) Temperature is the derivative of the partition function

d) Partition function is the integral of the temperature

**Answer: ** c) Temperature is the derivative of the partition function

What is the Maxwell-Boltzmann distribution used to describe?

a) The distribution of energies in a gas of classical particles

b) The distribution of energies in a gas of quantum particles

c) The distribution of particles in a quantum system

d) The distribution of particles in a classical system

**Answer: ** a) The distribution of energies in a gas of classical particles

What is the Fermi-Dirac distribution used to describe?

a) The distribution of energies in a gas of classical particles

b) The distribution of energies in a gas of quantum particles

c) The distribution of particles in a quantum system

d) The distribution of particles in a classical system

**Answer: ** c) The distribution of particles in a quantum system

What is the Bose-Einstein distribution used to describe?

a) The distribution of energies in a gas of classical particles

b) The distribution of energies in a gas of quantum particles

c) The distribution of particles in a quantum system

d) The distribution of particles in a classical system

**Answer: ** b) The distribution of energies in a gas of quantum particles

What is the relation between the partition function and the entropy?

a) Partition function is equal to entropy

b) Entropy is the logarithm of the partition function

c) Entropy is the derivative of the partition function

d) Partition function is the integral of the entropy

**Answer: ** b) Entropy is the logarithm of the partition function

What is the equipartition theorem in statistical mechanics?

a) It states that energy is equally distributed among particles in a system

b) It states that temperature is inversely proportional to energy

c) It states that entropy is directly proportional to energy

d) It states that pressure is directly proportional to energy

**Answer: ** a) It states that energy is equally distributed among particles in a system

What is the relation between the partition function and the pressure?

a) Partition function is equal to pressure

b) Pressure is the logarithm of the partition function

c) Pressure is the derivative of the partition function

d) Partition function is the integral of the pressure

**Answer: ** c) Pressure is the derivative of the partition function

What is the relation between the chemical potential and the number of particles in a system?

a) Chemical potential is equal to the number of particles

b) Number of particles is the logarithm of the chemical potential

c) Number of particles is the derivative of the chemical potential

d) Chemical potential is the integral of the number of particles

**Answer: ** c) Number of particles is the derivative of the chemical potential

What is the principle of detailed balance in statistical mechanics?

a) It states that the microstates of a system are equally probable

b) It states that the macroscopic properties of a system do not change over time

c) It states that the rates of forward and backward processes are equal in equilibrium

d) It states that the entropy of a system is constant over time

**Answer: ** c) It states that the rates of forward and backward processes are equal in equilibrium

What is the relation between the entropy and the number of microstates in a system?

a) Entropy is equal to the number of microstates

b) Number of microstates is the logarithm of the entropy

c) Number of microstates is the derivative of the entropy

d) Entropy is the integral of the number of microstates

**Answer: ** b) Number of microstates is the logarithm of the entropy

What is the thermodynamic limit in statistical mechanics?

a) The limit where the number of particles in a system approaches infinity

b) The limit where the temperature of a system approaches zero

c) The limit where the volume of a system approaches zero

d) The limit where the pressure of a system approaches infinity

**Answer: ** a) The limit where the number of particles in a system approaches infinity

What is the relation between the chemical potential and the entropy in a system?

a) Chemical potential is equal to entropy

b) Entropy is the logarithm of the chemical potential

c) Entropy is the derivative of the chemical potential

d) Chemical potential is the integral of the entropy

**Answer: ** c) Entropy is the derivative of the chemical potential

What is the principle of maximum entropy in statistical mechanics?

a) It states that the entropy of a system is maximized in equilibrium

b) It states that the temperature of a system is maximized in equilibrium

c) It states that the pressure of a system is maximized in equilibrium

d) It states that the chemical potential of a system is maximized in equilibrium

**Answer: ** a) It states that the entropy of a system is maximized in equilibrium

What is the relation between the partition function and the Gibbs free energy?

a) Partition function is equal to Gibbs free energy

b) Gibbs free energy is the logarithm of the partition function

c) Gibbs free energy is the derivative of the partition function

d) Partition function is the integral of the Gibbs free energy

**Answer: ** b) Gibbs free energy is the logarithm of the partition function

What is the relation between the partition function and the chemical potential?

a) Partition function is equal to chemical potential

b) Chemical potential is the logarithm of the partition function

c) Chemical potential is the derivative of the partition function

d) Partition function is the integral of the chemical potential

**Answer: ** c) Chemical potential is the derivative of the partition function

What is the equiprobability postulate in statistical mechanics?

a) It states that all microstates are equally probable

b) It states that all macrostates are equally probable

c) It states that all particles have equal energy

d) It states that all particles have equal momentum

**Answer: ** a) It states that all microstates are equally probable

What is the relation between the partition function and the heat capacity?

a) Partition function is equal to heat capacity

b) Heat capacity is the logarithm of the partition function

c) Heat capacity is the derivative of the partition function

d) Partition function is the integral of the heat capacity

**Answer: ** c) Heat capacity is the derivative of the partition function

What is the relation between the partition function and the average energy of a system?

a) Partition function is equal to average energy

b) Average energy is the logarithm of the partition function

c) Average energy is the derivative of the partition function

d) Partition function is the integral of the average energy

**Answer: ** c) Average energy is the derivative of the partition function

What is the relation between the partition function and the fugacity?

a) Partition function is equal to fugacity

b) Fugacity is the logarithm of the partition function

c) Fugacity is the derivative of the partition function

d) Partition function is the integral of the fugacity

**Answer: ** c) Fugacity is the derivative of the partition function

What is the principle of ergodicity in statistical mechanics?

a) It states that a system will explore all possible states over time

b) It states that a system will stay in a single state forever

c) It states that the total energy of a system is conserved

d) It states that the entropy of a system is constant over time

**Answer: ** a) It states that a system will explore all possible states over time

What is the relation between the partition function and the fugacity coefficient?

a) Partition function is equal to fugacity coefficient

b) Fugacity coefficient is the logarithm of the partition function

c) Fugacity coefficient is the derivative of the partition function

d) Partition function is the integral of the fugacity coefficient

**Answer: ** b) Fugacity coefficient is the logarithm of the partition function

What is the relation between the partition function and the grand canonical potential?

a) Partition function is equal to grand canonical potential

b) Grand canonical potential is the logarithm of the partition function

c) Grand canonical potential is the derivative of the partition function

d) Partition function is the integral of the grand canonical potential

**Answer: ** b) Grand canonical potential is the logarithm of the partition function

What is the relation between the partition function and the grand canonical ensemble average?

a) Partition function is equal to grand canonical ensemble average

b) Grand canonical ensemble average is the logarithm of the partition function

c) Grand canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the grand canonical ensemble average

**Answer: ** d) Partition function is the integral of the grand canonical ensemble average

What is the relation between the partition function and the canonical ensemble average?

a) Partition function is equal to canonical ensemble average

b) Canonical ensemble average is the logarithm of the partition function

c) Canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the canonical ensemble average

**Answer: ** c) Canonical ensemble average is the derivative of the partition function

What is the relation between the partition function and the microcanonical ensemble average?

a) Partition function is equal to microcanonical ensemble average

b) Microcanonical ensemble average is the logarithm of the partition function

c) Microcanonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the microcanonical ensemble average

**Answer: ** b) Microcanonical ensemble average is the logarithm of the partition function

What is the principle of detailed balance in statistical mechanics?

a) It states that the rates of forward and backward processes are equal in equilibrium

b) It states that the entropy of a system is maximized in equilibrium

c) It states that the temperature of a system is maximized in equilibrium

d) It states that the pressure of a system is maximized in equilibrium

**Answer: ** a) It states that the rates of forward and backward processes are equal in equilibrium

What is the relation between the partition function and the heat capacity?

a) Partition function is equal to heat capacity

b) Heat capacity is the logarithm of the partition function

c) Heat capacity is the derivative of the partition function

d) Partition function is the integral of the heat capacity

**Answer: ** c) Heat capacity is the derivative of the partition function

What is the relation between the partition function and the average energy of a system?

a) Partition function is equal to average energy

b) Average energy is the logarithm of the partition function

c) Average energy is the derivative of the partition function

d) Partition function is the integral of the average energy

**Answer: ** c) Average energy is the derivative of the partition function

What is the relation between the partition function and the fugacity?

a) Partition function is equal to fugacity

b) Fugacity is the logarithm of the partition function

c) Fugacity is the derivative of the partition function

d) Partition function is the integral of the fugacity

**Answer: ** c) Fugacity is the derivative of the partition function

What is the relation between the partition function and the grand canonical potential?

a) Partition function is equal to grand canonical potential

b) Grand canonical potential is the logarithm of the partition function

c) Grand canonical potential is the derivative of the partition function

d) Partition function is the integral of the grand canonical potential

**Answer: ** b) Grand canonical potential is the logarithm of the partition function

What is the relation between the partition function and the grand canonical ensemble average?

a) Partition function is equal to grand canonical ensemble average

b) Grand canonical ensemble average is the logarithm of the partition function

c) Grand canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the grand canonical ensemble average

**Answer: ** d) Partition function is the integral of the grand canonical ensemble average

What is the relation between the partition function and the canonical ensemble average?

a) Partition function is equal to canonical ensemble average

b) Canonical ensemble average is the logarithm of the partition function

c) Canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the canonical ensemble average

**Answer: ** c) Canonical ensemble average is the derivative of the partition function

What is the relation between the partition function and the microcanonical ensemble average?

a) Partition function is equal to microcanonical ensemble average

b) Microcanonical ensemble average is the logarithm of the partition function

c) Microcanonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the microcanonical ensemble average

**Answer: ** b) Microcanonical ensemble average is the logarithm of the partition function

What is the principle of detailed balance in statistical mechanics?

a) It states that the rates of forward and backward processes are equal in equilibrium

b) It states that the entropy of a system is maximized in equilibrium

c) It states that the temperature of a system is maximized in equilibrium

d) It states that the pressure of a system is maximized in equilibrium

**Answer: ** a) It states that the rates of forward and backward processes are equal in equilibrium

What is the relation between the partition function and the heat capacity?

a) Partition function is equal to heat capacity

b) Heat capacity is the logarithm of the partition function

c) Heat capacity is the derivative of the partition function

d) Partition function is the integral of the heat capacity

**Answer: ** c) Heat capacity is the derivative of the partition function

What is the relation between the partition function and the average energy of a system?

a) Partition function is equal to average energy

b) Average energy is the logarithm of the partition function

c) Average energy is the derivative of the partition function

d) Partition function is the integral of the average energy

**Answer: ** c) Average energy is the derivative of the partition function

What is the relation between the partition function and the fugacity?

a) Partition function is equal to fugacity

b) Fugacity is the logarithm of the partition function

c) Fugacity is the derivative of the partition function

d) Partition function is the integral of the fugacity

**Answer: ** c) Fugacity is the derivative of the partition function

What is the relation between the partition function and the grand canonical potential?

a) Partition function is equal to grand canonical potential

b) Grand canonical potential is the logarithm of the partition function

c) Grand canonical potential is the derivative of the partition function

d) Partition function is the integral of the grand canonical potential

**Answer: ** b) Grand canonical potential is the logarithm of the partition function

What is the relation between the partition function and the grand canonical ensemble average?

a) Partition function is equal to grand canonical ensemble average

b) Grand canonical ensemble average is the logarithm of the partition function

c) Grand canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the grand canonical ensemble average

**Answer: ** d) Partition function is the integral of the grand canonical ensemble average

What is the relation between the partition function and the canonical ensemble average?

a) Partition function is equal to canonical ensemble average

b) Canonical ensemble average is the logarithm of the partition function

c) Canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the canonical ensemble average

**Answer: ** c) Canonical ensemble average is the derivative of the partition function

What is the relation between the partition function and the microcanonical ensemble average?

a) Partition function is equal to microcanonical ensemble average

b) Microcanonical ensemble average is the logarithm of the partition function

c) Microcanonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the microcanonical ensemble average

**Answer: ** b) Microcanonical ensemble average is the logarithm of the partition function

What is the principle of detailed balance in statistical mechanics?

a) It states that the rates of forward and backward processes are equal in equilibrium

b) It states that the entropy of a system is maximized in equilibrium

c) It states that the temperature of a system is maximized in equilibrium

d) It states that the pressure of a system is maximized in equilibrium

**Answer: ** a) It states that the rates of forward and backward processes are equal in equilibrium

a) Partition function is equal to heat capacity

b) Heat capacity is the logarithm of the partition function

c) Heat capacity is the derivative of the partition function

d) Partition function is the integral of the heat capacity

**Answer: ** c) Heat capacity is the derivative of the partition function

a) Partition function is equal to average energy

b) Average energy is the logarithm of the partition function

c) Average energy is the derivative of the partition function

d) Partition function is the integral of the average energy

**Answer: ** c) Average energy is the derivative of the partition function

a) Partition function is equal to fugacity

b) Fugacity is the logarithm of the partition function

c) Fugacity is the derivative of the partition function

d) Partition function is the integral of the fugacity

**Answer: ** c) Fugacity is the derivative of the partition function

a) Partition function is equal to grand canonical potential

b) Grand canonical potential is the logarithm of the partition function

c) Grand canonical potential is the derivative of the partition function

d) Partition function is the integral of the grand canonical potential

**Answer: ** b) Grand canonical potential is the logarithm of the partition function

a) Partition function is equal to grand canonical ensemble average

b) Grand canonical ensemble average is the logarithm of the partition function

c) Grand canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the grand canonical ensemble average

**Answer: ** d) Partition function is the integral of the grand canonical ensemble average

a) Partition function is equal to canonical ensemble average

b) Canonical ensemble average is the logarithm of the partition function

c) Canonical ensemble average is the derivative of the partition function

d) Partition function is the integral of the canonical ensemble average

**Answer: ** c) Canonical ensemble average is the derivative of the partition function