Thermodynamics

A theory is the more impressive the greater the simplicity of its premises, the more diverse the things it relates, and the more extended its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content which, I am convinced, . . . will never be overthrown - Albert Einstein

So far, we have been looking at chemistry from a microscopic scale upwards, starting with the electron, proton, and neutron, and working our way up to the molecules. In this fashion we learned to understand and predict what happens on a macroscopic scale. In thermodynamics we will look at matter from the another point of view. We will consider only the macroscopic properties of matter. Thermodynamics is a unique theory because it looks only at the macroscopic properties of matter and, on that basis alone, tries to predict what other macroscopic behavior exists. (e.g., whether a particular reaction will occur or not occur under certain conditions). It is based on a few basic tenets and is a general theory. In fact, if the entire atomic theory of matter were overthrown (i.e., electrons, neutrons, protons, atoms, molecules), the foundations of thermodynamics would still be sound. There are many things, however, that thermodynamics doesn't tell us. For example, while thermodynamics tells us that diamonds at atmospheric pressure will transform into graphite, it doesn't tell us how long for that transformation to occur.

To best understand the application of thermodynamics to chemistry we will first review some important general concepts. Scientists like to divide or cut the whole universe into smaller parts, and then study (and hopefully understand) the smaller parts. In the science of thermodynamics things are no different and we begin by distinguishing between our system of interest and its surroundings.

  System: The part of the universe under study.
  Surroundings: Everything else that can interact with the system.

In chemistry, the system is often the reactants and products of the chemical reaction, and surroundings will be some kind of container and everything outside the container. The surroundings may even include a solvent in which the reactants and products are dissolved.

Associated with a system are intensive and extensive properties.

  Extensive Properties are linearly dependent on amount of substance. For example, Mass, Volume, Energy
  Intensive Properties don't depend on amount of substance. For example, Temperature, Pressure, and Density

Remember, when two identical systems are brought together extensive properties will double in value, and intensive properties will stay the same.


Q: Is surface area an extensive property?


The First Law of Thermodynamics

The first law of thermodynamics is also known as the "Law of Conservation of Energy".

  First Law: Energy can be converted from one form to another but can be neither created nor destroyed.

Energy is classified into one of two forms:
  Potential Energy: Depends on object's position or composition
  Kinetic Energy: Depends on object's motion, that is, Ekinetic = ½mv2, where m and v are the object's mass and velocity, respectively.

Consider the example of a marble rolling in a bowl.

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At any instant in time, t, the marble has a potential energy given by

Epotential = mgh(t)

Here g is the acceleration constant due to gravity. The kinetic energy, at any instant in time t is given by

Ekinetic = ½ mv2(t)

When the marble is at the maximum height, hmax, its potential energy will be at a maximum, and its kinetic energy at a minimum (i.e., v = 0). As the marble rolls down the side of the bowl, its potential energy gets converted into kinetic energy (i.e., its velocity increases from zero). As the marble passes through h=0, that is, the bottom of bowl, the marble's potential energy will be at a minimum, and its kinetic energy at a maximum (i.e., maximum velocity). In the absence of friction, the marble would continue rolling up and down forever with its energy converting back and forth between potential and kinetic, and the total energy would remain constant.

Etotal = mgh(t) + ½mv2(t)

In the real world, where there is friction between the marble and the bowl, the marble eventually stops rolling. Since energy must be conserved, where did the energy go? The answer is that it gets dissipated into the marble and the bowl, that is, it is transferred to the internal energy associated with random atomic motion inside the marble and the bowl. Therefore, if we want to correctly describe this situation and obey the first law of thermodynamics, then we need to include the internal energy, U, of the system (marble and bowl) in our expression for the total energy of the system:

Etotal = U(t) + mgh(t) + ½mv2(t)

Note: While most scientists, including myself, prefer to use the symbol U to represent internal energy, be aware that some texts (including the online quizzes used here) also use E for the internal energy.

Work

By lifting the marble up to start it rolling we put energy into the marble. This type of energy transfer into our system is called work. Work is not a form of energy, but rather it is a process in which energy is transferred between the system and its surroundings.

  Work is an energy transfer process.

In physics we learn that work can be calculated given the Forces applied on an object over a given distance.

Work = (Force) $\times$ (distance applied)

As we just noted, the friction between the marble and the bowl causes the energy that we initially transferred into the system (marble and bowl) as work (i.e., lifting the marble and starting it rolling) to be eventually transferred (i.e., dissipated) to the internal energy of the marble and the bowl. So, when the system comes to equilibrium (i.e., the marble stops rolling) we will find that the internal energy of the system (marble and bowl) has increased.

Because energy must be conserved, the difference in the internal energy of the system (marble and bowl) before we lift the marble and start it rolling, and after it comes to equilibrium (i.e., stops rolling), must be equal to the work we performed on the system.

ΔU = Ufinal - Uinitial = w work performed on the system.

In this example, the initial and final states of the system look the same to the naked eye, that is, a marble sitting on the bottom of the bowl and not rolling. However, on closer inspection, one would noticed that the marble and bowl of the final state will have a slightly higher temperature due to the increased internal energy. Temperature is a measure of the degree of random motion of the atoms and molecules in a particular substance.

Heat

Another way we could obtain the same change in internal energy of the system (marble and bowl) is to heat the system. That is, by placing it in contact with an object that has a higher temperature, such as a hot plate, until we get the same change in temperature of the system that we obtained by performing work on the system.

  Heat is energy transfer by means of a temperature difference between system and surroundings.

ΔU = Ufinal - Uinitial = q heat is energy transferred

Just like work, Heat is not a form of energy, but rather, is an energy transfer process.

Heat is not a substance but you will often hear or read (erroneously) about it as though it is. "Putting heat into a substance" really means putting energy into a substance by the energy transfer process of heat.

In summary, there are only two forms of Energy: (1) Kinetic and (2) Potential, and there are only two ways to transfer energy: (1) Work and (2) Heat. Any change in energy of a system arises from the heat, q, and work, w, done on the system.

ΔU = q + w

State Functions

We've just seen two different ways to obtain identical changes in the internal energy of a system. That is, we can increase the internal energy using work, or using heat. Either way, the internal energy of final state is the same. When a property of the system does not depend on the history of the system (i.e., whether heat, work or both were employed), but rather, only its initial and final states, then it is called a state function.

State Function: Property of a system that does not depend on the previous history of the system, only its present condition.

The internal energy is an example of a state function. For example, the difference in internal energy between a liter of water in equilibrium at 10°C and 1 atmosphere, and a liter of water in equilibrium at 75°C and 2 atmospheres is the same no matter how many times the liter of water was heated and cooled down and the pressure changed while moving between the two equilibrium states. In contrast, heat and work are not state functions. Without knowing a system's history we cannot know how much energy was lost or gained by a system in the form of heat or work. Other state functions are

ΔV = Vf - Vi
Change in Volume
ΔT = Tf - Ti
Change in Temperature

Sign Conventions

We define a positive ΔU > 0 to mean that the system has gained energy from its surroundings, and a negative ΔU < 0 to mean that the system lost energy to its surroundings.

More specifically we define:
  q > 0 to mean energy was added to the system as heat.
  w > 0 to mean energy was added to the system as work.
  q < 0 to mean energy was lost from the system as heat.
  w < 0 to mean energy was lost from the system as work.

In chemistry we define the reactants and products as our thermodynamic system. Thus we define a chemical reaction according to its sign of q.

  Exothermic Reaction: Reaction that gives off energy as heat to its surroundings, that is, q < 0.
  Endothermic Reaction: Reaction that absorbs energy as heat from its surroundings, that is, q > 0.

Note: These quizzes use E, instead of U for the internal energy

  • Definitions of Terms - q, w, U:
  • Calculate ΔU from q and w:
  • Calculate ΔU Involving Electrical, Heat Energy and PV Work:

Homework from Chemisty, The Central Science, 10th Ed.

5.1, 5.4, 5.6, 5.9, 5.11, 5.15, 5.17, 5.23, 5.25, 5.29