Thermal Physics Year 2

What is an extensive variable?

A property which scales with the amount of material

What is an intensive variable?

A property that is independent of the amount of material

What are 2 examples of extensive materials?

Mass and volume

What are 2 examples of intensive materials?

Temperature and pressure

What does “thin walls” imply?

Constant temperature - container and outside world are in thermal equilibrium

What does a function of state depend on?

Depend only on the current state of the system, not its history

What do functions such as work done and heat depend on?

The path taken, they are not functions of state

What do equations of state describe?

The relationship between the state functions

What is the ideal gas law?

What is heat?

Thermal energy in transit

What is temperature a measure of?

Internal energy of a body

What is the zeroth law of thermodynamics?

If two bodies A and B are in thermal equilibrium with each other, and a third body C is in equilibrium with A, then C is also in equilibrium with B

What is the equation for the first law of thermodynamics and what do the symbols mean?

U is internal energy, Q is heat supplied TO the system, and W is work done ON the system

What is the equation for the work done on an expanding gas?

What is an exact differential and what is it denoted by?

dU is an exact differential, it is path dependent

What is an inexact differential and what is it denoted by?

(d bar)U is inexact, depends on the path taken between the limits

What is heat capacity?

The amount of heat that must be supplied to raise its temperature by 1K

Define C_V

Define C_P

What is the relationship between C_P and C_V?

What is the adiabatic constant in terms of C_V and C_P?

What is the principle of equipartition of energy?

each independent quadratic energy term contributes an amount 0.5kT to the total thermal energy

What is the heat capacity of a system?

The amount of heat that must be supplied to raise its temperature by 1K

What are the two equations associated with the adiabatic expansion/compression of an ideal gas?

What is the equation for work done in isothermal compression/expansion?

What is the equation for work done in adiabatic expansion/compression?

What is the Van der Waals equation of state for non-ideal gases 

In the Van der Waals equation of state for non-ideal gases, what are b’ and a’?

What does the Van der Waals equation of state for non-ideal gases account for that the ideal gas law doesn’t?

Finite volume of atoms/molecules

Interactions between molecules

Describe Van der Waals isotherms

Above a critical temperature, isotherms similar to an ideal gas

Below critical temperature, isotherms are distorted

Where is the critical temperature on this graph?

By definition, what does the critical point correspond to for a Van der Waals isotherm?

What is the partial differential expression that the critical point of a Van der Waals equation corresponds to?

What is the equation for T_c ? (where C is the critical point of a Van der Waals isotherm)

What is the equation for V_c ? (where C is the critical point of a Van der Waals isotherm)

What is the equation for p_c ? (where C is the critical point of a Van der Waals isotherm)

What are the three equivalent statements of the second law of thermodynamics?

No process is possible whose sole result is the transfer of heat from a colder body to a hotter body

No process is possible whose sole result is the complete conversion of heat into work

No heat engine operating between two temperatures T_H and T_C can be more efficient than a Carnot engine

What is an equation for internal energy of an ideal gas in terms of degrees of freedom?

U = (f/2) (NkT)

What is Clausius’ theorem for a reversible closed cycle?

What is Clausius’ inequality for any cycle?

What is the definition of entropy?

What is the entropy change around a closed reversible cycle?

0

Along a reversible adiabatic path what is the change in entropy?

0

What is the change in entropy for an isothermal change of state?

where Q is the heat transferred into the sysy

What is the entropy statement of the second law?

A process cannot occur if it would result in a decrease in the total entropy of the universe

What does the central equation of thermodynamics/the thermodynamic identity represent?

The first law written in a path independent form in terms of entropy changes

What is the expression for the central equation of thermodynamics/the thermodynamic identity?

What is the equation for ∆S(system) for a reversible expansion?

∆S(system, rev) = nR ln (Vf/Vi)

What is the equation for ∆S(system) for an irreversible Joule expansion?

∆S(system, irrev) = nR ln (Vf/Vi)

What is the equation for ∆S(surroundings) for a reversible expansion?

∆S(surroundings, rev) = -nR ln (Vf/Vi)

What is the equation for ∆S(surroundings) for an irreversible Joule expansion?

∆S(surroundings, irrev) = 0

What is the equation for ∆S(Universe) for a reversible expansion?

∆S(Universe)=0

What is the equation for ∆S(Universe) for an irreversible Joule expansion?

∆S(Universe)= nR ln(Vf/Vi)

What is the change in internal energy for a reversible expansion?

dU=0

What is the change in internal energy for an irreversible Joule expansion?

dU=0

What is the equation for dW for a reversible expansion?

dW = -pdV

What is the equation for dW for an irreversible Joule expansion?

dW=0

What is the equation for dQ for a reversible expansion?

dQ = -dW = pdV

What is the equation for dQ for an irreversible Joule expansion?

dQ = 0

For an irreversible, adiabatic process of mixing two ideal gases, what is the equation for change in entropy?

What is the Gibbs paradox?

If ∆S = -nR(x ln x + (1-x)ln (1-x)) then what would the change in entropy be if gas 2 were the same as gas 1?

What is a microstate?

One of many possible states of a system

(for a coin, heads or tails would be the microstate)

What is a macrostate?

What is the binomial distribution?

What is Stirling’s approximation?

For very large N, what is the most probable macrostate?

The observed/equilibrium state

What is the boltzmann relation?

S = k_B ln W

What is the equation for the number of ways to distribute N atoms amongst M cubic lattice sites?

What is the equation for change in entropy for the microscopic view of a lattice gas?

What is the equation for change in entropy for the macroscopic view of a VdW gas?

What are the constants in the microcanonical ensemble?

NVE

What are the constants in the canonical ensemble?

NVT

True or false, the first law in the form dU=TdS-pdV contains only state functions

True

What is the equation for fraction of defects, N/M?

What is the equation for internal energy in terms of N?

U = Nε

What is the equation for entropy as a function of the parameter?

What are defects in a crystal?

Sites that are missing an atom

What does the energy at which changes in a system occur most rapidly correspond to?

As T→0, ε>>kT, how does the system behave?

System highly ordered

Entropy has minimal effect

Energy penalty of defect dominates the physics

N/M→∞

As T→∞, ε«kT, how does the system behave?

System disordered

Entropy dominates the physics

Energy penalty has minimal effect

N/M=1/2

What are the assumptions of the model for crystal defects?

Only counted number of ways of choosing which N atoms are defect atoms

What is each atom also has the choice of M interstitial sites

Two contributions to the entropy:

• Number of ways of choosing atoms to be defects

• Number of ways that the defect atoms can be placed in interstitial sites

It is reasonable to assume that two adjacent defects have the same energy penalty to two separated defects

What is the probability of a microstate is proportional to the Boltzmann factor?

What is the equation for the partition function?

What is the state function equation of internal energy from the partition function?

What is the state function equation of specific heat from the partition function?

What is the state function equation of Helmholtz free energy from the partition function?

What is the state function equation of entropy from the partition function?

What is the equation for distinguishable particles?

What is the equation for the particle partition function for particles that exist in one of two states with energies?

What does the Dulong-Petit law incorrectly predict?

Predicts that the heat capacity of solids does not depend on temperature (spoiler alert it does)

What is the equation for the Einstein temperature?

ω is dependent on the type of atom 

What is the equation for the Lennard-Jones potential

What is the equation for the internal energy of the Einstein solid?

What is the equation for the entropy of the Einstein solid writing K=M-1

What is the number of quanta in the Einstein solid as a function of temperature?

What is the internal energy of the Einstein solid?

What is the Einstein solid partition function?