C2301 Midterm 2 Flashcards
What are the levels of energy separations in quantum mechanics?
Etrans>Erot>Evib>Eelec
What is the relative probability of finding a molecule in a corresponding energy state called?
The Boltzmann Distribution
What are Degrees of Freedom?
The number of variables needed to describe the motion of a particle completely.
Degrees of Freedom for Translational Motion
3 (x,y,z)
Degrees of Freedom for Rotational Motion
Linear: 2
Nonlinear: 3
Degrees of Freedom for Vibrational Motion:
Linear: 3N-5
Nonlinear: 3N-6
Define heat
The amount of E that flows across a boundary of 2 objects due to a temperature difference.
What is the spontaneous direction of flow for heat?
High T - Low T
What are the 3 ways heat is transferred?
- Convection
- Conduction
- Radiation
Transitory Property
Only appears during a change of state of system; not related to initial and final states. Path function. Ex) Heat
Heat capcity
the measure of E needed to change the temperature of a substance a given amount.
Dependent on material and temperature.
Extensive quantity
Depends on amount and nature of material
Heat capacity at constant pressure (eqn)
Cp=dqp/dT
Heat capacity at constant volume (eqn)
Cv=dqv/dT
Shomate equation (Explanation)
Describes the heat capacity of a material as a function of temperature, where the coefficients were determined from curve fitting.
How are Cp,m and Cv,m related for gases? (eqn)
Cp,m=Cv,m+R
Why is Cp>Cv for gases?
In a constant pressure process, gas expands as its T increases, and the system does work on the surroundings. As a consequence, not all of the heat flow into the system can be used to increase dU. In constant volume, no work occurs; thus, all heat is used to increase dU.
How are Cp and Cv related for liquids and solids?
Cp is approximately equal to Cv.
Why are Cp and Cv approximately equal for liquids and solids?
Any volume change upon heating is negligible.
What quantity represents heat at constant volume?
delta U
What quantity represents heat at constant pressure?
delta H
What is a fundamental relation in defining the other relations, which connects internal energy change, volume, pressure, and heat?
dU=d_q-pdV
where d_q is an inexact differential
Define enthalpy
Enthalpy is measured as the heat transfer by the system for a process occuring at constant pressure.
How can Cv,m be used to find heat?
qv=nCv,mdT
where d represents delta T
How can Cp,m be used to find heat?
qp=nCp,mdT
where d represents delta T
What assumptions are made when relating Cv and Cp to other quantities in a cycle?
We assume no chemical reactions or phase changes occur.
Also assume Cv and Cp are constant over the temperature change occuring.
What can we say about isobaric processes?
w=-PextdV
where dV=Vf-Vi
What can we say about isochoric processes?
w=0 and dU=q
What can we say about isothermal processes?
dT=0 and dU=dH=0
What can we say about adiabatic processes?
q=0 and dU=w
What can we say about the internal energy in a closed cycle
dUcycle=0
Relations for reversible adiabatic systems
PiVi^y=PfVf^y
(Tf/Ti)=(Vf/Vi)^1-y
where y=Cp/Cv
How can we set up the equations for an irreversible adiabatic system?
dU=w
nCv,mdT=-Pext(Vf-Vi)
Can carry the above forward to solve for Tf in terms of Pf, Pi, Pext, and Cv,m.
What does reversible adiabatic compression lead to in terms of T?
Heating
What does reversible adiabatic expansion lead to in terms of T?
Cooling
Thermochemistry
Concerned with heat flow into or out of a reaction system
Endothermic
A reaction where E is absorbed by the system
Exothermic
A reaction where E is released by the system.
What is the E stored in chemical bonds referred to as?
Potential E
What is typical standard state?
1 bar, 25C (298.15K)
Standard enthalpy of formation
enthalpy change of a rxn in which only 1 mol of the species of interest, with only pure elements in their most stable states under standard conditions appear as reactants.
Hess’s Law
the enthalpy change for any sequence of chemical rxns that sum to the overall rxn is the same as that of the base rxn.
What parameters are held constant in O2 bomb calorimetry?
Volume
What reaction happens in O2 bomb calorimetry?
Combustion
How is the calorimetry constant, Ccal, determined?
A standard (usually benzoic acid) of known molar enthalpy of combustion can be obtained to accurately determine the heat capacity constant of the bomb calorimeter.
How can internal energy be calculated in oxygen bomb calorimetry?
dU=ms/MsdUc+mH2O/Mh20CpdT+CcaldT=0
What is another name for constant pressure calorimetry?
Coffee-cup calorimetry
What assumptions can be made for solids and liquids when used in constant pressure (or volume) calorimetry?
dH is approximately equal to dU
List the names of all phase transitions of matter.
Can refer to pg 14 of unit 3 notes.
Start of unit 4 notes
What are the two main state functions and path functions in unit 4?
State: U and H
Path: q and w
What is the result if we multiply the following partial differentials together: dP/dT x dV/dT x dT/dP
-1
What is the name of the coefficient denoted alpha?
Isobaric volumetric thermal expansion coefficient
What symbol denotes the isothermal compressibility?
Kappa sub T
What is the differential equation that relates the change in U with T and V?
dU=(dU/dT)dT+(dU/dV)dV
where italics represent partials
What is the internal pressure relation?
dU/dV=T(dP/dT)-P
What is the internal P of an ideal gas?
0
What was the Joule experiment?
Attempted to measure dU/dV for an ideal gas.
Describe the experimental apparatus of the Joule experiment.
Consider it has two interacting systems in a rigid adiabatic enclosure. The 2 systems are 1) water bath and 2) volume within left and right glass bulbs. These together are isolated.
Look further into this experiment
What was the Joule-Thomson Experiment?
Seeked to measure dH/dV and is far more accurate than the previous experiment.
Explain the Joule-Thomson experiment and apparatus.
Gas flows from a high-pressure cylinder into a low-pressure cylinder. Gas is forced through a porous plug in which the piston moves to maintain a constant pressure, until all of the gas has been transferred through the plug.
What is the result of the Joule-Thomson experiment?
After transfer of gas, there is a large pressure drop across the plug and the temperature change of the gases can be measured. This is an adiabatic process.
What remains constant for the process in the Joule-Thomson experiment?
Enthalpy; isoenthalpic.
Joule-Thomson coefficient
limiting ratio of dT and dP; experimentally determined; denoted u_J-T
What dominates when u_J-T is positive?
Attraction
What dominates when u_J-T is negative?
Repulsion
What happens when P is decreased for positive Joule-Thomson coefficients?
Gas is cooled
What happens when P is decreased for negative Joule-Thomson coefficients?
Gas is heated
Inversion Temperature
u_J-T=0
When can dH be determined by measuring qp? (3)
- Any arbitrary process at constant P
- In a closed system
- Where only P-V work is carried
Heat capacity at constant P (differential definition)
Cp=dH/dT
If Cp is constant, dHp can be represented by this simplified formula:
dHp=nCp,mdT
What is the approximation for enthalpy of solids and liquids (assuming they are a function of T alone)?
dH=n integral,Ti-Tf(Cp,mdT)
What are the 2 statements/formulations of the second law?
- It is impossible for a system to undergo a cyclic process that turns all heat completely into work done on the surroundings.
- It is impossible for a process to occur that has the sole effect of removing a quantity of heat from an object at lower T and transferring it to an object at higher T.
Classical definition of entropy
Entropy is the amount of E not available to do work
Definition of entropy (differential eqn form)
dS=dqrev/T
What is the spontaneous heat flow according to entropy?
Higher q to lower q (dq<0)
What is the following sentence termed?
For any process that proceeds in an isolated system, there is a unique direction of spontaneous change and dS>0 for the spontaneous process.
The 2nd Law of Thermodynamics
Is S positive or negative for expansion?
+
Is S positive or negative for compression?
-
Is entropy a path or state function?
State
What is the entropy for phase changes?
dvapS=dvapH/Tvap
What is the statistical definition of entropy?
Entropy is a measure of the degree to which E is dispersed into the available E levels associated with random molecular motion of all molecules in a system
What is a single particle microstate?
Any particular E state of a single molecules, i.e. its quantized unit, which is combined translational, rotational, and vibrational E states
N-particle microstate
Any quantized state of a whole system of molecules.
Consists of the single particle microstates of all molecules.
What are the 5 rules for the number of N-particle microstates?
- At any given instant in time, the total E is dispersed throughout one N-particle microstate.
- In the next instant, Etot is in a different N-p.m. of equal energy.
- Each accessible equal E N-p.m. is equally possible for the system
- The number of single particle microstates for a single molecule is large, and for N-particle microstates is enormus.
- Under a given set of conditions, the number of accessible N-p.m. is the number of ways its thermal E can be dispersed among the trans, rot, and vib E levels of all its molecules
What is the Ludwig Boltzmann eqn?
S=kBln(omega)
If entropy is positive, did the system transition from smaller N-p.m. (initial) to larger N-p.m. (final) or the reverse case?
Smaller-larger
What conclusions were made based on the statistical entropy approach to the spontaneous isothermal expansion of a gas?
dEn is inversely proportional to the square of the length of a 1D box.
How can entropy be calculated in an isothermal process?
dSsys=nRln(Vf/Vi)
How can the entropy change in the surroundings be found?
dSsurr=dqsurr/T= -dqsys/T
What condition is required so that the entropy of a system can decrease in a spontaneous process?
dStotal>0
Why is entropy often called Time’s arrow?
For an isolated system, entropy can only increase, not decrease; i.e. spontaneous systems lead to an increase of Stotal.
3rd Law of Thermodynamics
The entropy of a pure, perfectly crystalline substance is zero at 0K
How many microstates are in a perfectly crystalline solid?
1
What is residual entropy?
The entropy at 0K for not perfectly ordered crystals
What is the order of magnitude of entropy among the phases of matter?
solid<liquid<gas
