Physical Chemistry Mock Midterm Exam

Physical Chemistry Mock Midterm Exam

**disclaimer: I have no idea exactly what will be on the midterm exam beyond what was listed by the professor in class, although I do know these section headings are accurate. This mock midterm is written only as a study tool. It’s usefulness is debatable.

Part I: Definitions (20%)

Provide definitions for each of the following terms. Do NOT give any examples of the terms or you will lose marks.  (1 mark per definition, -1 mark if example given)

1) System:

2) Isolated system:

3) closed system:

4) open system:

5) surroundings:

6) Zeroth Law of Thermodynamics:

7) Thermal Energy:

8) Internal Energy:

9) Heat:

10) Work:

11) First Law of Thermodynamics:

12) Reversible Path:

13) Nonreversible Path:

14) State Function:

15) Heat Capacity (also include definition for molar heat capacity and specific heat capacity):

16) Translational State (strongly doubt this would actually be asked because not defined in lecture):

17) Rotational State:

18) Vibrational State:

19) Equiparition of Energy:

20) Bond Energy

21) Hess’s Law:

22) Heat of Formation of a Molecule:

22) Heat of Combustion of a Molecule:

23) Enthalpy:

26) State: 

Part II: Calculations

Provide all work, including appropriate equations, notation, and manipulation.

Try (or retry) calculations from the textbook without looking at the solutions manual.

For a good selection of questions do:

Energy, Heat, Work

3, 4, 6, 10

Thermochemistry

15, 17, 21, 24, 29, 32, 34

Equiparitioning of Energy

1)   Calculate the number of degrees of freedom for carbon dioxide. Estimate the molar heat capacity of the substance.

2)   Calculate the number of degrees of freedom for methane. Estimate the molar heat capacity of the substance.

Part III: Short Answers

1)   What type of system is a coffee cup calorimeter? What type of system is a bomb calorimeter? Compare and contrast.

2)   If system A is 25ºC and system B is 25ºC, and system C is in equilibrium with system B, what can we conclude about the temperature of system C and its relationship with system A?

3)   Draw potential energy diagram of a diatomic molecule. Label the place of greatest repulsion, A. Label the place of greatest stability, B. Label zero point, C. Label and show the bond energy. Draw in the largest state (rotational/vibrational/translational) , and discuss the placement and magnitude of the other states (rotational/vibrational/translational).

4)   Is the maximum work done by the system reversible or irreversible? Explain referring to a P versus V diagram.

5)   Using the definition of enthalpy, show that it is equal to the heat at constant pressure.

6)   Define both the heat capacity at constant volume and the heat capacity at constant pressure.

7)   Is work a state function? Explain.

8)   Discuss how differential calorimetry finds the unknown heat capacity of a substance.

9)   What is the standard enthalpy of formation of oxygen gas?

10) Why is the bond energy always positive?

11) Hydrogen gas only has 2 rotational degrees of freedom. Explain why.

12) Discuss the effects of temperature when comparing calculated heat capacities using equiparitioning of energy and the actual measured heat capacity values.

Part IV: True or False

This section will NOT be on the exam, however, it may provide a good snapshot as to whether the definitions are understood.

1)   Heat leaves the system. q is positive.             True/False

2)   Energy is stored in chemical bonds.             True/false 

3)   The system does work. w is negative.             True/false

4)   Internal energy does not depend on PV work.             True/false

5)   Bond energy is usually greater than thermal energy.             True/false

6)   A diatomic gas has 2 degrees of translational energy.             True/false

7)   PV work is positive for an expansion of a gas.             True/false 

8)   The lowest vibrational state is at the zero point.             True/false 

9)   The heat capacity at a phase change is infinite.            True/false

10)  Vibrational states are the same as angular momentum.             True/false 

Part V: Bonus Questions

1)   Show that PV=nRT is a state function using partial derivatives and Euler’s Theorem for Exactness without referring to Appendix C. (Just kidding! Bad joke, I know.) (Yes, I am actually joking about this one, don't try to solve it!)

2)   Describe your experience and opinion of the textbook with regards to whether you have the e-book or hardcopy, its acquisition and availability, its use as a study tool, and to what extent it corresponds to and complements the lectures.

Equiparitioning of Energy

This post is designed to explain how to calculate the various degrees of freedom of translational, rotational, and vibrational energy in a molecule, and and calculate heat capacity from these values with equiparitioning of energy.

Let's start by defining internal energy of a molecule:

The bond energy usually dominates the thermal energy with a much bigger value, so we often neglect the thermal energy. However, heat capacity depends only on thermal energy, NOT bond energy, so it is important for something.

Translational Energy

The translational energy is defined as 

I will offer an explanation as to where this definition came from later, but until I update this post, I suggest checking both http://www.chem.queensu.ca/people/faculty/mombourquette/firstyrchem/GasLaws/KMT.htm

and section 1.9 from the text book. (My laziness is because I am incredibly hungry and tired.) 

The translational energy is partitioned among three degrees of freedom along the three cartesian axes. 

Rotational Energy

The rotational energy also is split up equally between three degrees of freedom. However, with a linear molecule, rotating it about the z-axis has insignificant energy as the mass of the molecule is almost completely in the atomic nuclei, so we only consider its rotation about the x- and y-axis.

A linear molecule has only two degrees of rotational freedom. 

A nonlinear molecule has three degrees of rotational freedom. 

Vibrational Energy

The vibrational energy can be resolved into a certain number of normal modes of vibration, known as its degrees of freedom. 

Summary of Degrees of Freedom

If a molecule has N atoms, 3N degrees of freedom must be specified. We have already defined the translational and rotational degrees of freedom for nonlinear and linear molecules. The vibrational degrees of freedom are merely the leftovers from the total. This is summarized in the table below: 

Heat Capacities Further Defined

Equiparition of energy states that each translational and rotational degree of freedom contains 1/2RT energy, of kinetic energy only. Each vibrational degree of freedom contains RT energy, which includes both the potential energy and kinetic energy. 

The heat capacities are given by multiplying the energy factor by the gas constant times the number of degrees of freedom. This gives a value in J/(mol*K), which is the unit for heat capacity. 

These formulae can be used to estimate the molar heat capacities of gases. The molar heat capacity of monatomic gases only depends on translational motion. For diatomic molecules, the translational and rotational components are more dominant than the vibrational components for determining the heat capacities. For anything larger, the calculated values are very far off the actual heat capicities. So instead of throwing our hands up in the air and praying to the quantum mechanic gods, mortals immortalized (Einstein and Stern) suggest that this extreme variation from the actual values is because equiparitioning breaks down at lower temperatures, especially for vibrational states. 

Why is that? Remember that vibrational levels are much more widely spaced than the rotational and translational levels. The larger gaps require a large quantum of energy to be supplied to move from one vibrational level to the next. This would sufficiently muck up our calculated values. However, at higher temperatures the calculated molar heat capacity values would have much better agreement with actual values, as more energy is supplied to the molecules. 

Summary: 

Molecules have various degrees of freedom which compose their thermal energy. These degrees of freedom are related to the heat capacity. By knowing the number of degrees of freedom and how energy is distributed between the degrees of freedom (translational, rotational and vibrational), we then can construct the heat capacities of the substance. 

At lower temperatures, the heat capacities calculated in this manner will not correspond with the actual heat capacities.

Because two hot plates are better than one...

How my TA instructed us to set up our distillation for the extraction of trimyristin from nutmeg lab.

Note the beaker set up to catch the water dripping from a leak in the tubing. 

Translational, Rotational, and Vibrational Energies

Energy from a molecule is not stored in chemical bonds. Rather it is stored in the translational, rotational, and vibrational energies of the molecule - the thermal energy.

The Potential Energy Diagram for a Diatomic Molecule

The states of a molecule are quantized and can be represented by a potential energy diagram. This potential energy diagram represents a diatomic molecule. On the x axis, we examine the internuclear distances between the two atoms. As the atoms approach an internuclear distance of zero, their potential energy is infinite. This is because the two atoms cannot occupy exactly the same point at the same time. Repulsion forces dominate, and there is no chemical bond. The point with the lowest potential energy of the graph is the ideal bond length of the diatomic molecule. Then, for increasing values of internuclear distance between the nuclei of the two atoms the potential energy increases and no bonding occurs as the attractive forces are too weak. Essentially, the two atoms are too far apart to have a bond. Note that when two atoms approach one another from infinite distance (righthand side of graph), the energy of the system is lowered.

This can be compared to you and a not so close friend sitting on a chesterfield (sofa, couch, whatever) together. Let's call your friend Matthew. If Matthew and you both sit on the far ends of the chesterfield, chances are you are less likely to have a conversation and be friendly together. Other elements in your environment aka other friends could come and sit between you both, and so you might be closer these other friends, and hence more engaged with them. This is analogous to no bonding at great distances. Now if you decide to sit on top of Matthew, he will not be very happy with you because he doesn't know you very well. Chances are he'll go all cactus mode and repel the physical contact. Sounds like what happens to two atoms with a internuclear distance approaching zero! However, to achieve the optimal comfort level, you would sit beside Matthew close enough to be friendly, but far enough away to respect both of your personal bubbles. Hence, you experiencing bonding at this distance.

Now the funky stripes on the potential energy diagram represent the vibrational energy of the molecule. The lowest vibrational state is above the minimum potential energy on the curve. Why? Well, according to the Heisenburg Uncertainty Principle, the both the bond length at equilibrium and the vibrational motion can not simultaneously be known. This point is called the zero point.

Taking a Closer Look

Let's zoom in on some of these vibrational states on the potential energy diagram.

We find in between them superimposable rotational states that also describe the state of the molecule. Even further in between these rotational states we find the translational states of the molecule. This is because

Now, I can't really use the Matthew analogy here, because a vibrating Matthew is just a very, very bad idea (yikes, did I actually just write that?), but I will attempt to explain in greater detail where on earth these states come from!

Molecular Quantum States

The states of a molecule are quantized. Here is how these various quantizations are defined (I realize the definitions here may be crude, however this is the level we are expected to understand for this course, so it isn't too elaborate.):

a) electronic states: recall the s, p, d, f orbitals for atoms. There is a similar method out there for molecular states.

b) rotational states: these the same as other angular momentum, like the angular momentum in orbitals. These are usually denoted by quantum numbers Jmj where J goes from 0 to infinity and -J < mj < +J . Spin also has angular momentum given by either +1/2 or -1/2.

c) vibrational states: go in integer values from v=0 to infinity.

d) translational states: can be eliminated by sitting on the frame reference of the molecule and hence are usually not of interest. This can be done by taking a frame of reference. For insistence if you bus from your apartment to St. Viateur bagel, the motion of the bus is counted as stationary if you consider the frame of reference of the bus. So if you "sit" on top of a molecule, its translational states can be ignored.

The states we examine in thermodynamics are all from the world of the macroscopic.
These states (electronic, rotational, vibrational, translational) discussed above are from the quantum world - the microscopic. However, since the lectures took a substantial aside in this direction to explain heat capacity as it is related to the thermal energy of the substance, the information above is probably relevant.

Chapter 2 Definitions for Chem 203

So our secret (or not so secret rather) instructions say that we need to write out a bunch of definitions for 20% of our midterm, and no examples can be given otherwise marks will be docked.

I'm going to include key terms from each of the lectures here. This list is most likely incomplete, but  I'm going to post what I have so far and add to it later. :) The main sources for these definitions were the lecture notes and the hardcopy of the textbook. And of course, wikipedia. cough, cough.

Lecture 1

system: that part of the universe of interest
open system: a system where matter or energy can flow into/out of the system
closed system: a system where energy can flow into/out of the system, but matter cannot
isolated system: neither matter nor energy can enter/exit the system, only move around inside

temperature: physical property related to the measure of the average kinetic energy of the atoms or molecules of a substance; degree of hotness of a body, substance, medium
thermal equilibrium: any flow of heat into or out of a body is equal to the flow of heat into or out of another body, the two bodies have the same temperature (also applies to more than two bodies)

exothermic: energy is released from the system, weaker bonds go to stronger bonds
endothermic: energy is absorbed by the system, stronger bonds go to weaker bonds

Zeroth Law of Thermodynamics: If system A is in equilibrium with system B and system B is in equilibrium with system C, then system A is in equilibrium with system C and A, B, and C have the same temperature.

state: defined by the parameters that are measured and describe a system under these conditions

Lecture 2 and 3

thermal energy: (this is really difficult to define, so the definition I provide is half-a**ed aka ambiguous from the prof's notes) the energy around us, part of the total internal energy of a thermodynamic system or sample of matter, partly the kinetic energy of the system's particles, equally partitioned between all degrees of freedom of particles (translational, vibrational, rotational), not a state function or property of a system as depends on path taken

*potential energy diagram*
I will discuss the BE diagram of a diatomic molecule in another post, as this shows up time after time and it might be important for the course. :) Yay!

cold temperatures: temperatures less than 1000-2000 K, restricts chemistry

internal energy: energy needed to create system from atoms, contains kinetic energy of motion (moving, rotating, vibrating), as well as electrostatic energy of the attraction and repulsion of electrons and nuclei [excludes PV work on the surroundings]

heat: transfer of energy from high to low temperature by conduction, radiation, convection; path dependent

work: energy transferred by a force acting on a distance; path dependent

PV work: 

state function: property of a system whose value does not depend on the path taken to reach that specific value, only dependent on initial and final conditions

reversible path: maintains equilibrium between the system and surroundings throughout the change from the initial state to the final state; most efficient path

non-reversible path: does not maintain equilibrium between the system and surroundings throughout the change from the initial state to the final state, cannot not be undone, inefficient

The First Law of Thermodynamics: U=q+w

Thermodynamics: gives relationships between states at equilibrium

Lecture 4

heat capacity: the amount of heat required to raise the temperature of any substance by 1 K; includes the ability for a substance to store energy the various degrees of freedom in movement/translation, rotation, and vibration of the particles

Enthalpy: H= U + PV

isochoric process: process occurring at constant volume (the internal energy is equal to the heat of the system)

isobaric process: process occurring at constant pressure (the enthalpy is equal to the heat of the system)

isothermal process: process occurring at constant temperature

Lecture 5

No vocab, just a proof dealio about state functions and Euler's criterion for exactness, which will not show up on the exam as involves material beyond the scope of the course.

Lecture 6

thermochemistry: study of the heats of reactions under various conditions

*bond energy diagram shows up again*

Lecture 7

equipartition of energy: in thermal equilibrium, the energy is shared equally among all of its various forms, such as translational, rotational, and vibrational components of a molecule
^
(stay tuned for an upcoming post about this long topic)


Lecture 8

bond energy: energy needed to break a bond, always positive as energy put into the system

Differential Scanning Calorimetry

This is just a quick post on something that was mentioned briefly in lecture. I strongly doubt that any type of calculation based question would be asked on a midterm, but perhaps a theory question could show up.

Differential Scanning Calorimetry is when you compare an unknown sample with a reference sample of known heat capacity at constant pressure. You choose a reference with a well-defined heat capacity over the range of temperatures scanned. Also, you choose a reference that will not undergo a phrase transition, as that will distort the results in regards to the sample. The differential scanning calorimeter is used to measure heat flow in the substances in either exothermic and endothermic reactions. It has the ability to measure phase transition temperatures and enthalpies, which makes it useful to create phase transition diagrams and the like.

Wasn't that terribly informative?

Infinite Heat Capacity?

How much heat is required to change ice at -10ºC into steam at 110ºC for one mole?

This is a favourite question by any thermal dynamics textbook. :)

First of all, we consider what happens at a phase change. At a phase change, the substance is applying all of the heat received into breaking the bonds, and hence, the temperature does not change. However, when the substance accepts heat and is not at a state change, the substance does increase in temperature. The important temperatures to consider, are of of course the melting point and the boiling point. Of water, we know they are 0ºC and 100ºC respectively.

Note that in these equations, one always is evaluating the difference in temperature. This type of calculation does not require conversion from Celsius to Kelvin as the difference will stay the same. (If you are skeptical, try it out! I only mention this as the question came up in lecture and seemed to be shared by many people.)

So returning to the initial question, how much heat is required?

This equation can be shown heuristically by a graph:

Now, examining the heat capacity of water at constant pressure at the phase changes we see a the following graph. This graph is a simplified version of the real relationship of heat capacity while applying heat to a substance, as the heat capacity between the phase change would not be constant. However, we consider it to be constant to simplify matters.

The intriguing part of the above graph is what happens to the heat capacity at the phase transition. The change in temperature is zero at these places. This can be expressed by:

The heat capacity is infinite at a phase change? What does this mean?

Recall, the system will absorb all of the heat given without changing the temperature, and so until the bonds are broken, it will happily accept ALL the heat provided. The heat capacity is infinite at the phase change, as the system has no limit for receiving heat.

Heat Capacity... Specifically

This post is to cover the various definitions of heat capacity. For a more thorough discussion of heat capacity, upcoming posts will examine some practical examples involving phase transitions, and finally delve into the components of heat capacity including a discussion about bond energies and degrees of freedom in molecular structure.

Before viewing this post, I recommend taking a look at my post entitled "Enthalpy Unleashed!" for a  comprehensive discussion about the First Law of Thermodynamics defined in terms of the Ideal Gas Law.

Formal Definitions of Heat Capacity

Before we jump into equations, let's define heat capacity by describing it in words.

Heat capacity defines a substance's ability to accept heat to raise its own temperature by a given amount. It is usually expressed in units Joule per Kelvin. This is an extensive property as it relies on sample size.

Also, you probably will run into something called specific heat capacity. This is given in units of mass times Joule per unit Kelvin, which causes it to be an intensive property, as it does not depend on the size of the substance of inquiry. Molar heat capacity is also an intensive property, as it is given in units of mole times Joule per Kelvin.

If this still seems too abstract, let's look at the term itself. Capacity is defined to be the maximum quantity that something can contain. For instance, if you fill your freezer with 200 bagels and discover you can't fit in anymore, your freezer has a capacity to hold 200 bagels. In contrast, if you slice your bagel for toasting and your toaster only has the space for two slices of bagel, we say the toaster has a capacity to hold 1 bagel. The capacity of the toaster is less than that of the freezer. Now, applying this idea to heat capacity, the heat capacity is the object's ability to hold heat. To quantify the heat accepted, we need to measure a change, which is done by examining the temperature change of the substance, since accepting heat will cause the molecules of the substance to vibrate more rapidly, invoking a temperature increase by the Kinetic Molecular Theory.

Now, with all that said and done, on with the integrals!

a) At constant volume, the internal energy is equal to the heat of the system. Integrating U with respect to temperature, we define the heat capacity to be

b) At constant pressure the enthalpy is equal to the heat of the system. Integrating H with respect to temperature, we define the heat capacity to be

Note that the heat capacity at constant volume is not equivalent to the heat capacity at constant pressure.

Enthalpy and the Ideal Gas in Terms of Heat Capacities

Recall the enthalpy equation written in terms of the Ideal Gas Law:

Integrating the above with respect to temperature gives:

And substituting in for the definitions of heat capacity expresses the equation as such: 

Success with Mr. Hess

This post is mainly because I've been playing around with some calculations involving Hess's Law with varying degrees of success. Chances are you were first introduced to these calculations in some type of general chemistry class or even high school, and problems provided a series of reactions that could be fit jigsaw puzzle style together to make the total enthalpy of formation of the desired chemical equation.  Now low and behold, the problems start withholding more of the puzzle pieces! Oh no!

Here is an example: 

Calculate (the enthalpy of formation) for methane with the given data: 

To calculate this, we first write down the desired chemical equation: 

Then we use the various enthalpy of combustion of both the products and reactants to find enthalpy of formation for methane. 

This is a rather tedious process, but hopefully a comprehensive one. 

Lament on Studying

To what capacity can this brain retain
As heated quantities and work maintain?
The pressure is constant, but volume increases
The flow continues and never ceases!
Isolated am I, but in a functional state
Yet I wish I would learn at a greater rate.

Enthalpy Unleashed!

Let's examine the First Law of Thermodynamics yet another time. In a previous post entitled "Another Work Out," we discussed the different conditions for a system to have no PV work. Exploring these conditions (constant volume and pressure) further, we will define the effects upon the internal energy and introduce a new state function, the enthalpy of the system.

Process At Constant Volume 

We consider the system to only have PV work. 

This scenario is commonly encountered in a bomb calorimeter, which will be explored in an upcoming post. 

But, hey wait a minute, we know the change in volume to be zero, as the volume is constant. 

So that was pretty straight forward. 

This process is irreversible by the way. 

Process At Constant Pressure

Let's check out the system under constant pressure with only PV work. Just a reminder that the pressure under study is the external pressure. The internal energy is still defined under the First Law: 

We solve for the heat at constant pressure and expand the equation: 

The significance of this little manoeuvre is to recognize that the heat at constant pressure is made up state functions, and hence is a state function itself. 

Now, we define the heat at constant pressure as the enthalpy of the system: 

It is important to realize that although the internal energy equals the heat at constant volume and the enthalpy equals the heat at constant pressure, both internal energy and enthalpy exist at conditions where the pressure and/or volume aren't constants. 

Alternative Way of Defining Enthalpy

As with many series of equations you can approach the derivation backwards. I realize this is a trivial addition to this post, but because enthalpy is kind of abstract when you are first introduced to it, I feel it may add to a thorough approach to understanding the definition. As I like both of these derivations equally - maybe because they are equal *groan* - and found them both useful study tools, here goes! 

Expand the equation, considering the system to be irreversible, so useful work is negligible, and the external pressure is constant. 

We can cancel a bunch of terms. The "w" work, which is equal to the nonPV work in the system, is zero. The middle terms cancel, and the change in the pressure is also zero, as the pressure is constant. So the one lone heat at constant pressure term remains, showing it to be the enthalpy, just as we expected. 

Hee. :)

Enthalpy for Reactions Involved in Consumption or Production of an Ideal Gas

Okay, this is just a little calculation trick for problem solving. 

So, here is our old friend, the Ideal Gas Law: 

Hm, doesn't that PV look really similar to the PV in the enthalpy equation? 

But the reaction occurs at constant temperature, so 

Just a quick tip on how to calculate the change in the number of moles of gas. First you will probably have to write out your balanced chemical equation. So far, the problems I have commonly seen involve combustion reactions of a liquid hydrocarbon. The water produced in a combustion is also treated as a liquid. Omit the liquid and/or reactants and products, and calculate the difference between the gaseous products and reactants only. 

This equation can also be defined in terms of heat capacities, but I will return to it in an upcoming post. Until then... good night. :P

Another Work Out

Work versus Energy

Work can come in many forms including mechanical, electrical, chemical, and biological work. This shouldn't be a big surprise considering that we measure it in units of Joules just like energy, and the mantra of many text books is that energy is neither created nor destroyed, it can only change forms. Why shouldn't there be different forms of work as well? In fact, the First Law of Thermodynamics, is just the Law of Conservation of Energy revamped.

However, one must admit it can be confusing to distinguish between work and energy. So here are the nitty-gritty details:

Energy is the potential for an object to produce or create work.
Work is defined as a force provided along a change in distance.

Consider a stationary bagel on a countertop. The bagel has potential energy calculated from the height of the countertop, but isn't doing any work. However, if you push said bagel to skim across the countertop (assume countertop and bagel are frictionless, this wouldn't work too well in practice!) the bagel will have kinetic energy as well as work.

Defining Work with Calculations

So here is the work equation from first year physics:

This can be represented in as an integral: 

**note that you are looking at a change in length.

Now, we are going to examine work with regards to a piston in a cylinder. I should really steal a photo of this from the web and stick it on this blog, but I'm sure many are available in your text book of choice. Pressure in this system is defined as: 

Substituting this back into the work integral gives: 

But note that area times length equals volume. So the equation is simplified to: 

And let it take place at constant pressure, so we can pull a constant from the integral. 

The equation needs to fit with our conventions that work done by the system is positive and work done on the system is negative, and so we place a negative sign in front of the equation. 

 Note that the pressure in this equation is always, always, always the external pressure, not the pressure of the gas.  At a reversible rate, the external pressure will equal the pressure of the gas. 

When is no work done? 

Interesting question. Or not. But still, the problems sets are probably going to test understanding of this concept, so let's examine it by letting the equation equal zero.

All right, so there are two options: 

No work is done when there is no external pressure so the reaction takes place in a vacuum, or when there is no volume change aka the system has constant volume. 

These two situations are irreversible paths. 

Isothermal Process: A Reversible Path

An isothermal process is where a system experiences a change under constant temperature (no temperature change). The internal energy change is zero, as the heat received is transferred directly into the work done on the gas, for example. 

How is a system like this possible without the system interacting with the temperature of the surroundings? As the Zeroth Law says heat flows from hot to cold until both bodies reach the same temperature. This situation seems far too idealistic to be true. 

First of all, remember that thermodynamics is about ideal relationships. In other words, it avoids facing reality. (Kay, maybe this was too harsh and untrue.) Secondly, various sources suggest that this type of process can occur in a carefully maintained heat bath through slow heat exchange. 

Anyway, the isothermal process is reversible.

And of course there is a handy formula derivation that goes with it; the results of which you can keep in your back pocket or arsenal supply, depending on your attitude and emotional outlook on this material.

It involves the Ideal Gas Law (with n=1) where 

So returning to the work equation

We substitute in the Ideal Gas definition for pressure

And the fun begins! (Don't forget temperature is a constant.) 

Recall that 

And applying this to the work equation gives

Recall that 

So the equation in final form can be written as 

Yipee! 

Forthcoming Posts and Plans

I wish to find an example of how to use the isothermal work equation, because I think that would be useful, so I will check my text book and various sources online, and possibly post a subsequent series of equations solved, as those in my class who can't download the prof's ebook, also can't readily download the solutions manual. The limitation to this is that equations I can't solve, I can't post. However, because typing equations is fairly time consuming with the lack-there-of programs I have, I will probably type up the problem from the book and provide a solution by means of a photograph of my notebook. 

Also, I intend to do further posts with topics and subtopics including processes at constant volume, processes at constant pressure, the enthalpy definition, calorimetry and heat capacity, so look out for those if you are interested. 

*The title of this post comes from a wonderful jazz album by the tenor saxophonist Hank Mobley. On this album is one of my favourite jazz recordings of all time entitled "I should care." This isn't related to thermodynamics, but it's pretty hot stuff.