What is the first law of thermodynamics?

Energy conservation principle: ΔU = ΔQ -ΔW.

Heat energy is the only form of energy that can do work.

The total energy in a closed system is always increasing.

Energy cannot be created or destroyed: E = mc².

State the second law of thermodynamics.

The total entropy of an isolated system always increases over time.

Energy cannot be created or destroyed.

Heat flows from cold to hot spontaneously.

The total energy of an isolated system remains constant.

Explain the concept of microstates in statistical mechanics.

Microstates are distinct configurations of a system's particles that correspond to a specific macroscopic state, crucial for understanding entropy in statistical mechanics.

Microstates are the visible states of matter in a system.

Microstates refer to the average energy of a system's particles.

Microstates are the total number of particles in a system.

What is a macrostate and how does it differ from a microstate?

A macrostate is a large-scale description of a system, while a microstate is a specific detailed configuration of that system.

A macrostate is a single configuration of a system, while a microstate is a general overview.

A macrostate refers to the smallest unit of a system, while a microstate is the overall behavior.

A macrostate is a random arrangement of particles, while a microstate is a fixed arrangement.

How does the third law of thermodynamics relate to absolute zero?

The third law of thermodynamics indicates that at absolute zero, the entropy of a perfect crystal is zero.

At absolute zero, all molecular motion ceases completely.

The third law implies that perfect crystals can exist at any temperature.

The third law states that entropy increases as temperature decreases.

Describe the concept of entropy in thermodynamics.

Entropy is a measure of disorder in a thermodynamic system.

Entropy is a measure of temperature in a system.

Entropy is a measure of energy in a system.

Entropy is the total energy of a thermodynamic system.

Aarush is conducting an experiment where he heats a gas in a sealed container. He notices that as the temperature of the gas increases, the particles inside the container move faster. What is the relationship between temperature and energy in statistical mechanics?

Temperature is directly proportional to the average kinetic energy of particles.

Temperature is unrelated to the motion of particles.

Temperature has no effect on the energy of particles.

Temperature is inversely proportional to the average kinetic energy of particles.

How does the concept of indistinguishability affect statistical mechanics?

Indistinguishability leads to different statistical distributions for identical particles, influencing their thermodynamic behavior.

Indistinguishability has no impact on particle interactions.

Indistinguishability is irrelevant in classical mechanics.

Identical particles behave differently only at high temperatures.

What role does the concept of equilibrium play in thermodynamics?

Equilibrium indicates a stable state where macroscopic properties are constant, crucial for energy and matter exchange.

Equilibrium is a condition where all reactions are halted.

Equilibrium is a state of constant temperature only.

Equilibrium refers to the absence of any energy transfer.

Explain how statistical mechanics connects microscopic and macroscopic properties of systems.

Statistical mechanics connects microscopic and macroscopic properties by averaging the behavior of particles to derive macroscopic quantities.

Statistical mechanics only focuses on macroscopic properties without considering microscopic behavior.

Statistical mechanics connects properties by analyzing only the largest particles in a system.

Microscopic properties are irrelevant to the understanding of macroscopic systems in statistical mechanics.

In a math game, Arnav calculates the probability of rolling a sum of 7 with two dice. How does this relate to statistical mechanics in physics?

Both involve calculating probabilities of different outcomes.

Math games use probability, but statistical mechanics does not.

Statistical mechanics only deals with certainties, not probabilities.

There is no relation between math games and statistical mechanics.

What is a spontaneous process ?

process that does not need external intervention to occur / keep happening

process that needs an external intervention to occur

Reversible processes are important in thermodynamics because

we can write thermodynamic equations only for reversible processes

all thermodynamic processes are reversible

we are not interested in irreversible processes

reversible processes are easy to understand

What does a single point in phase space represent?

The average state of the system

The most probable state of the system

What is the significance of a macrostate in statistical mechanics?

It corresponds to a set of microstates having the same thermodynamic properties.

It describes the positions and momenta of individual particles.

It is a single configuration of the system.

It is not related to thermodynamics.

Which of the following correctly defines the number of accessible microstates in a given phase space volume?

Ω=Total Volume of Phase Space/Volume of a Phase Cell

Ω=Number of Particles/Volume of Phase Space

What does Liouville’s theorem state about the phase space density function ρ?

It remains constant along the trajectory of the system.

It increases exponentially with time.

It depends on the ensemble type.

What does it mean if the Poisson bracket {ρ,H}=0?

The density function ρ is time-independent.

The density function is necessarily uniform.

The system is in a microcanonical ensemble.

In the microcanonical ensemble, the phase space density function ρ is typically:

A function of the Hamiltonian H

If a function f has a Poisson bracket {f,H}=0, what can be inferred about f?

(a) It is a constant of motion.

(b) It must be a function of H.

(c) It is necessarily equal to zero.

In equilibrium, what does the phase space trajectory look like?

It fills the entire energy surface.

It fills a small localized region.

What does this equation signify in phase space?

Equation of a sphere of radius sqrt(2mE) in 3N dimensional momentum space

Equation of a sphere of radius sqrt(2mE) in N dimensional momentum space

Equation of a sphere of radius sqrt(2mE) in 3 dimensional momentum space

Equation of a sphere of radius sqrt(2mE) in 6N dimensional phase space

Asher is conducting an experiment with a gas in a closed container. He notices that during a cyclic process, the internal energy change, dU, is observed. What is the energy change, dU in this cyclic process?

depends on the radius of indicator diagram

A cyclic process is performed on a gas where the PV diagram is a triangle. How does the net work done depend on the area of the triangle?

Work done is equal to the area of the triangle

Work done is equal to the perimeter of the triangle

Work done is proportional to the number of particles

For a cyclic process in a PV diagram, if the cycle is traversed in a clockwise direction, what does it signify?

The system does positive work on the surroundings

The change in internal energy is negative

The surroundings do positive work on the system

What does a phase space hypersurface represent?

A set of microstates satisfying a constraint

A collection of all possible macrostates

The time evolution of a thermodynamic variable

A region where entropy remains constant

Why does phase space volume matter in quantum statistical mechanics?

It helps in determining entropy of the system

It limits the number of allowed quantum states or accessible microstates

total volume of accessible phase space is dependent on the Hamiltonian or energy constraint of the system

Statistical Mechanics

Authored by Preetika Dhawan

Physics

University

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50 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

System is said to be in thermodynamic equilibrium when it is in ......

Mechanical equilibrium

Thermal equilibrium

Chemical equilibrium

All above

MULTIPLE CHOICE QUESTION

1 min • 1 pt

................... remains constant during the adiabatic process

Volume

Temperature

Entropy

Density

MULTIPLE CHOICE QUESTION

1 min • 1 pt

All natural processes are

Isothermal

Adiabatic

Reversible

Irreversible

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Heat engine convert heat into

Light energy

Mechanical energy

Electrical energy

Magnetic energy

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following is reversible process

Carnot Heat Engine

free expansion of gas

Heat conduction

Rubbing of stones

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The entropy of universe tending to

Minimum

Zero

Maximum

Constant

MULTIPLE CHOICE QUESTION

1 min • 1 pt

We apply statistics for

a single particle problem

for many particle problem

for two particle problem

for many dissimilar particles

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Statistical Mechanics

System is said to be in thermodynamic equilibrium when it is in ......

................... remains constant during the adiabatic process

All natural processes are

Heat engine convert heat into

Which of the following is reversible process

The entropy of universe tending to

We apply statistics for

Thermodynamic variables are

Thermodynamic potentials has the dimension of..

What are thermodynamic potentials

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