Exam1

The thermodynamic condition under which the change in enthalpy is equal to the heat transferred into a system.

Constant pressure

The entropy is associated with what qualitative feature of a system?

A measure of disorder

List two general categories (types) of energy storage at the atomic and molecular level, for subsequent access by cellular biochemistry.

(1) Chemical reactions [bond formation and breaking]

(2) Chemical bonding and interactions [molecular recognition]

A property that does not depend on the size of the system, such as temperature.

Intensive quantity

Ideal monatomic gas

A gas in which the constituent atoms do not interact with each other.

State the first law of thermodynamics in words (no equations).

Conservation of energy

Three physical quantities related through the first law of thermodynamics.

Internal energy; heat transfer; work

An experimental process in which a system can exchange energy with a heat bath.

Isothermal

An alternative term for mechanical work in thermodynamics expressed in terms of intensive and extensive variables.

PV work

Thermodynamic quantity used as an effective measure of the stored potential energy of a molecular system.

Heat capacity at constant pressure, Cp

In an empirical force field for a protein, what type of function is used to approximate the region of the potential well for interacting covalently-bonded atoms along the protein backbone?

Harmonic oscillator

The weakest form of intermolecular interaction.

van der Waals interaction

Normalization factor for the Boltzmann distribution.

Partition function

The difference between the ground state of a molecule and its first excited state is known as

Energy gap

The van der Waals interaction potential between two carbon atoms in an amino

acid depends on the dihedral angle between the planes formed by adjacent covalent bonds. t f

False [van der Waals interactions depend only on the distance between two interacting atoms]

Which of Newton’s laws of motion is used to compute the force on an atom from an empirical potential energy surface? You can write it out in words or symbols.

Newton’s Second Law; Force = mass x acceleration, or F = ma [ok if vector notation for F and a is not used].

(a) What is the approximate value of ε for water

[unitless in the form of Coulomb’s law we will use, from the text]? This effect is not as strong in the interior of a protein. (b) What is the approximate value of ε in the interior of a protein

(providing a range is ok).

ε ~ 80 in water solvent; ε ~ 2-4 in the interior of the protein

Given M trials of a binary yes/no event, what is the mathematical expression for computing the probability P(M,N) of observing N “yes” events, if the probability of a single “yes” event is p?

P(M,N) = W(M,N) x pN x (1-p)M-N where W(M,N) is the multiplicity

The number of different molecular configurations consistent with macroscopic thermodynamic parameters.

Multiplicity

The most likely thermodynamic state of a system corresponds to maximizing entropy.

False Entropy maximization

According to the third law of thermodynamics discussed in class, at T = 0 K (273.15 C), the entropy S = 0. Apply the statistical expression for the entropy to rationalize why this should be the case

[brief answer].

S = k ln W, and at T=0 there is no motion, so the system is frozen into a single configuration

(microstate) => W = 1. Thus, S = k ln W = k ln 1 = 0.

Three alternative formulations of entropy.

Statistical, thermodynamic, probabilistic

The entropy is an extensive state function. What feature of the natural logarithm (ln) function discussed in class makes ln W (where W = multiplicity) appropriate for defining the entropy, rather than W alone?

The fact that the logarithm of a product is equal to the SUM of the logarithms. This preserves the extensive character of the entropy, since the multiplicity W of a combined system is the product of the multiplicities of the subsystems.

[True or False] The work done in a near-equilibrium expansion of an ideal gas is less than the work done for a nonequilibrium expansion.

False

[True or false] Consider a coin with two sides (H = heads; T = tails). The probability of observing HHHHHTTTTT is equal to the probability of observing HTHTHTHTHT.

True [order of appearance of H’s in throws doesn’t matter].

What are the two types of multiplicity that—in general—need to be considered for molecular systems?

configurational and energetic

State the 2nd law of thermodynamics in words (complete sentence).

The entropy of a combined system + its surroundings always increases for a spontaneous process.

The energy multiplicity for a system of identical molecules is given by the formula

where N = total # of molecules, t = # of energy levels available for occupation, and Ni is the number of molecules having energy Ui. What is the physical reason for the factorial factors appearing in the denominator of this expression?

For a given energy level UI (the ith energy level), the Ni molecules having that energy are indistinguishable. The Ni ! for that particular (ith) level corrects for this overcounting.

The main variable appearing in the probabilistic definition of the entropy is the probability that a given energy level pi with energy Ui, is occupied. Write an expression for pi in terms of the number of molecules Ni having energy Ui, and the total number of molecules in the system, N.

pi = Ni /N

In the probabilistic expression for the entropy S, the probability of a particle occupying the ith energy level is denoted by pi. What two features of a) the pi and b) the probabilistic expression itself guarantee that the entropy S will always be positive?

The pi are all positive and less than 1, since they represent probabilities that must be normalized (sum to) 1.

2) Since the ln of a positive number less than 1 is always negative (property of the logarithm function), each ln pi term contributes a negative number, which cancels the overall minus sign in S, making the entropy overall positive.

A system of Ar atoms has a positional multiplicity of 350 and an energy multiplicity of 5. Assuming that interactions between the rare gas atoms can be neglected, what is the total multiplicity?

1750

Define what is meant by an energy distribution.

An energy distribution is a specification of the # of particles (atoms, molecules…)---i.e. the population---in each allowed energy level. It reflects the aggregate probability of finding molecules in different energy levels.

Define the energy multiplicity of an energy distribution.

Energy multiplicity = # of equivalent arrangements of system particles that result in the same energy distribution.

[True or False] Spontaneous heat transfer between two systems is driven by minimization of the total system multiplicity.

False. It is driven by maximizing the multiplicity, which corresponds to maximizing the entropy.

What is the name (in words) and variable (symbol) given to the multiplicative factor in the Boltzmann distribution to assure proper normalization of the energy level probabilities? Give both for full credit.

partition function, Q

What is the mathematical property of the exponential function that makes it consistent with both the statistics of a many-particle system, and fixed total energy U of the system?

eA x eB = eA+B

[Fill in the blank] Consider the statement: “Microstates associated with a given thermodynamic macrostate that have the same energy, number of particles, and occupy the same total volume are equally likely to occur in that macrostate.” This statement is known as

the principle of equal a priori probabilities

The Boltzmann distribution describes the energy distribution of system particles at what thermodynamic state of the system?

Equilibrium

What is the fundamental relation of thermodynamics?

dU = TdS – PdV.

[True or false] If a system is in thermal equilibrium, it is also in thermodynamic equilibrium.

False. Note, however, that the converse statement (thermodynamic equilibrium implies thermal equilibrium) is true.

What is the zeroth law of thermodynamics?

“Existence of temperature” OR “Systems that are each in thermal equilibrium with a separate, reference system are in thermal equilibrium with each other.”

[Fill in the blank] The intensive variable conjugate to the (extensive) entropy is …………………………

temp

What type of chemical bonding plays a key role in defining protein secondary structure?

Hydrogen bonding

True or false: The effective charges of the atoms in a protein structure are uniquely defined by their underlying quantum mechanical interactions.

False [the values depend on the environment and the specific decomposition scheme used, as illustrated in the Rappe’ and Goddard figure shown in lecture].

As the number of events in a statistical trial increases, do unlikely outcomes become more or less rare?

more rare

[Fill in the blank] What is the name of the continuous mathematical function that can be used to approximate the discrete expression for the probability P in question #1?

Gaussian distribution