3. Thermodynamics

The zeroth law of thermodynamics is based on a simple observation: when one object is in thermal equilibrium with another object, say a cup of warm tea and a metal stirring stick, and the second object is in thermal equilibrium with a third object, such as your hand, then the first and third object are also in thermal equilibrium.

As such, when brought into thermal contact, no net heat will flow between these objects. Note that thermal contact does not necessarily imply physical contact, as objects can be in thermal contact across space.

The formulation of the zeroth law—that no net heat flows between objects in thermal equilibrium, and the corollary that heat flows between two objects not in thermal equilibrium—actually arose from studies of temperature. At any given time, all substances have a particular temperature. In everyday language, we use the term temperature to describe qualitatively how hot or cold something is, but in thermodynamics, it has a more precise meaning. At the molecular level, temperature is proportional to the average kinetic energy of the particles that make up the substance.

At the macroscopic level, it is the difference in temperature between two objects that determines the direction of heat flow. When possible, heat moves spontaneously from materials that have higher temperatures to materials that have lower temperatures. Heat itself refers to the transfer of thermal energy from a hotter object with higher temperature (energy) to a colder object with lower temperature (energy). If no net heat flows between two objects in thermal contact, then we can say that their temperatures are equal and they are in thermal equilibrium.

The first law is really just a particular iteration of the more universal physical law of energy conservation: energy can be neither created nor destroyed; it can only be changed from one form to another. Because the first law accounts for all work and all heat processes impacting the system, the presence of nonconservative forces poses no problem because the energy transfer associated with friction, air resistance, or viscous drag will be accounted for in the first law equation.

For example, when a car "burns rubber," all the smoke and noise coming from the back tires is a clear indication that mechanical energy is not being conserved. However, if we include the energy transfers associated with the frictional forces in our consideration of the change in internal energy of the system, then we can confidently say that no energy has been lost at all: there may be a "loss" of energy from the car as a result of the friction, but that precise amount of energy can be "found" elsewhere—as thermal energy in the atoms and molecules of the surrounding road and air.

Now, think about what happens when one adds heat to ice that is at 0°C. The heat energy causes the water molecules to begin to move away from each other by breaking free of the hydrogen bonds between them. Because the water molecules are being held less rigidly in place, they now have greater degrees of freedom of movement and their average potential energy increases. In statistical mechanics, one would say that this increased freedom of movement permits a greater number of microstates for the water molecules.

For example, instead of only being able to move up and down or sway side-to-side, a water molecule may now have more freedom of movement and be able to rock forward and back. In gaining additional directions and forms of motion, however, the amount of up-and-down or side-to-side motion must decrease, thus keeping the average kinetic energy of liquid water at 0°C the same as solid water at 0°C. In summary, while liquid water may have a greater number of microstates due to increased freedom of movement, its average kinetic energy is the same as solid water at the same temperature.

When describing processes, physicists often use terms such as natural, unnatural, reversible, or irreversible. These terms confuse students but needlessly so because these terms are descriptive of observable phenomena.

For example, we expect that when a hot object is brought into thermal contact universe system surroundings with a cold object, the hot object will transfer heat energy to the cold object until both are in thermal equilibrium (that is, at the same temperature). This is a natural process and also one that we would describe as irreversible: we are not surprised that the two objects eventually reach a common temperature, but we would be shocked if all of a sudden the hot object became hotter and the cold object became colder. This would be an unnatural process.

KEY CONCEPT 4

Heat is the process of energy transfer between two objects at different temperatures and will continue until the two objects come into thermal equilibrium at the same temperature.

As discussed earlier in this chapter, the zeroth law of thermodynamics says that objects in thermal contact are in thermal equilibrium when their temperatures are the same. The corollary of this is the second law of thermodynamics: objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature at thermal equilibrium.

Heat, then, is defined as the process by which a quantity of energy is transferred between two objects as a result of a difference in temperature. As we will discuss further in our examination of the second law, heat can never spontaneously transfer energy from a cooler object to a warmer one without work being done on the system.

During any thermodynamic process, a system goes from some initial equilibrium state with an initial pressure, temperature, and volume to some other equilibrium state, which may be at a different final pressure, temperature, or volume. These thermodynamic processes can be represented in graphical form with volume on the x-axis and pressure (or temperature) on the y-axis.

In each of these cases, some physical property is held constant during the process. These processes are isothermal (constant temperature, and therefore no change in internal energy), adiabatic (no heat exchange), and isovolumetric (no change in volume, and therefore no work accomplished; also called isochoric). Isobaric processes are those that occur at a constant pressure. Because the work on a P-V graph is simply the area under the curve, the work done in this closed-loop process is the area inside the loop.

KEY CONCEPT 5

One calorie (little c) is the amount of heat required to raise 1 g of water one degree Celsius. One Calorie (big C) is the amount of heat required to raise 1 kg of water 1 degree Celsius, equal to 1000 calories.

KEY CONCEPT 2

Temperature is a physical property of matter related to the average kinetic energy of the particles. Differences in temperature determine the direction of heat transfer.

Since the 18th century, scales have been developed to quantify the temperature of matter with thermometers. Some of these systems are still in common use, including the Fahrenheit (°F), Celsius (°C), and Kelvin (K) scales. Fahrenheit and Celsius are the oldest scales still in common use and are relatively convenient because they are based on the phase changes for water, as shown in Table 3.1. In the Celsius scale, 0° and 100° define the freezing and boiling temperatures of water. In the Fahrenheit scale, these phase change temperatures are defined as 32° and 212°.

The Kelvin scale is most commonly used for scientific measurements and is one of the seven SI base units. It defines as the zero reference point absolute zero, the theoretical temperature at which there is no thermal energy, and sets the freezing point of water as 273.15 K. The third law of thermodynamics states that the entropy of a perfectly-organized crystal at absolute zero is zero. Note that there are no negative temperatures on the Kelvin scale because it starts from absolute zero. Although the Kelvin and Celsius scales have different zero reference points, the size of their units is the same. That is to say, a change of one degree Celsius equals a change of one unit kelvin. Because there are 180 degrees between water's phase changes on the Fahrenheit scale, rather than 100 degrees as on both the Celsius and the Kelvin scales, the size of the Fahrenheit unit is smaller.

Consider each of the following scenarios: hot tea cooling down, a frozen drink melting, iron rusting, buildings crumbling, balloons deflating, and living things dying and decaying. These scenarios share a common denominator. In each of them, energy of some form is going from being localized or concentrated to being spread out or dispersed. The thermal energy in the hot tea is spreading out to the cooler air that surrounds it. The thermal energy in the warmer air is spreading out to the cooler frozen drink.

The chemical energy in the bonds of elemental iron and oxygen is released and dispersed as a result of the formation of the more stable, lower-energy bonds of iron oxide (rust). The potential energy of the building is released and dispersed in the form of light, sound, and heat as the building crumbles and falls. The energy of the pressurized air is released to the surrounding atmosphere as the balloon deflates. The chemical energy of all the molecules and atoms in living flesh is released into the environment during the process of death and decay.

The SI unit for heat is the joule (J), which should not be surprising because it is based on energy. Heat can also be measured in the units of calorie (cal), nutritional Calorie (Cal), or the British thermal unit (BTU). The nutritional Calorie ("big C") is not the same thing as the calorie ("little c"); one Calorie is equal to 1000 calories or 1 kcal.

The conversion factors between the units of heat are as follows: 1 Cal ≡ 10 cal = 4184 J = 3.97 BTU

KEY CONCEPT 3

The first law of thermodynamics tells us that an increase in the total internal energy of a system is caused by transferring heat into the system or performing work on the system. The total internal energy of a system will decrease when heat is lost from the system or work is performed by the system.

The phase change from liquid to solid (freezing or solidification) or solid to liquid (melting or fusion) occurs at the melting point. The corresponding heat of transformation is called the heat of fusion.

The phase change from liquid to gas (boiling, evaporation, or vaporization) or gas to liquid (condensation) occurs at the boiling point. The corresponding heat of transformation is called the heat of vaporization.

A system is the portion of the universe that we are interested in observing or manipulating.

The rest of the universe is considered the surroundings.

It has long been noted that some physical properties of matter change when the matter gets hotter or colder. Length, volume, solubility, and even the conductivity of matter change as a function of temperature. The relationship between temperature and a physical property of some matter was used to develop the temperature scales with which we are familiar today. For example, Daniel Fahrenheit developed the temperature scale that bears his name by placing a thermometer filled with mercury into a bath of ice, water, and ammonium chloride. The cold temperature caused the mercury to contract, and when the level in the glass tube stabilized at a lower level, he marked this as the zero reference on the scale. He then placed the same mercury thermometer in a mixture of ice and water (that is, at the freezing point for water).

The slightly warmer temperature of this mixture caused the mercury to rise in the glass column, and when it stabilized at this higher level, Fahrenheit assigned it a value of 32°. When he stuck the thermometer under his (or someone else's) tongue, he marked the even higher mercury level as 100° (not 98.6°). The details of how and why Fahrenheit came to choose these numbers (and the history of their adjustment since Fahrenheit first developed the scale) are beyond the scope of this discussion; rather, what is important to note is that a change in some physical property of one kind of matter—in this case, the height of a column of mercury—can be correlated to certain temperature markers, such as the phase changes for water. Once the scale has been set in reference to the decided-upon temperature markers, then the thermometer can be used to take the temperature of any other matter, in accordance with the zeroth law.

KEY CONCEPT 6

The universe is a closed, expanding system, so you know that the entropy of the universe is always increasing. The more space that appears with the expansion of the universe, the more space there is for the entire universe's energy to be distributed and the total entropy of the universe to increase irreversibly.

KEY CONCEPT 1

The zeroth law of thermodynamics states the transitive property in thermal systems: If a = b and b = c , then a = c .

To define a reversible reaction, let's consider a system of ice and liquid water in equilibrium at 0°C. If we place this mixture of ice and liquid water into a thermostat (device for regulating temperature) that is also at 0°C and allow infinitesimal amounts of heat to be absorbed by the ice from the thermostat so that the ice melts to liquid water at 0°C and the thermostat remains at 0°C, then the increase in the entropy of the system (the water) will be exactly equal to the entropy decrease of the surroundings (the thermostat). The net change in the entropy of the system and its surroundings is zero.

Under these conditions, the process is reversible. The key to a reversible reaction is making sure that the process goes so slowly—requiring an infinite amount of time—that the system is always in equilibrium and no energy is lost or dissipated. To be frank, no real processes are reversible; we can only approximate a reversible process. Note how physicists define reversible processes: These are processes that can spontaneously reverse course. For example, while water can be put through cycles of freezing and melting innumerable times, ice melting on the warm countertop would not be expected to suddenly freeze if it remains in the warm environment. The liquid water will need to be placed in an environment that is cold enough to cause the water to freeze, and once frozen in the cold environment, the ice would not be expected to begin melting spontaneously. The freezing and melting of water in real life are therefore irreversible processes in physics while still being chemically reversible.

When a substance is undergoing a phase change, such as from solid to liquid or liquid to gas, the heat that is added or removed from the system does not result in a change in temperature. In other words, phase changes occur at a constant temperature, and the temperature will not begin to change until all of the substance has been converted from one phase into the other. For example, water melts at 0°C. No matter how much heat is added to a mass of ice at 0°C, the temperature of the equilibrated system will not rise until all the ice has been melted into liquid water.

We've determined that adding heat raises the temperature of a system because the particles in that system now have a greater average kinetic energy, and it's true that molecules have greater degrees of freedom of movement in the liquid state than in the solid state (and even more so in the gas state). However, phase changes are related to changes in potential energy, not kinetic energy. The molecules of water in ice, for example, aren't truly frozen in place and unable to move. The molecules rotate, vibrate, and wiggle around. The bonds within each molecule are also free to bend and stretch. Of course, the molecules are held in relatively stable positions by the hydrogen bonds that form between them, but they still have a fairly significant amount of kinetic energy. The potential energy, however, is quite low because of the stability provided by the relative closeness of one molecule to another and by the hydrogen bonds.

Closed systems

are capable of exchanging energy, but not matter, with the surroundings. The classic experiments involving gases in vessels with movable pistons are examples of closed systems. For thermodynamic purposes, most of what will be encountered on Test Day will be a closed system or will approximate a closed system.

Isolated systems

are not capable of exchanging energy or matter with their surroundings. As a result, the total change in internal energy must be zero. Isolated systems are very rare, although they can be approximated. A bomb calorimeter attempts to insulate a reaction from the surroundings to prevent energy transfer, and the entire universe can be considered an isolated system because there are no surroundings.

State functions

are thermodynamic properties that are a function of only the current equilibrium state of a system. In other words, state functions are defined by the fact that they are independent of the path taken to get to a particular equilibrium state. The state functions include pressure (P), density (ρ), temperature (T), volume (V), enthalpy (H), internal energy (U), Gibbs free energy (G), and entropy (S). On the other hand, process functions, such as work and heat, describe the path taken to get to from one state to another.

Open systems

can exchange both matter and energy with the environment. In an open system, not only does the matter carry energy, but more may be transferred in the form of heat or work. A boiling pot of water, human beings, and uncontained combustion reactions are all examples of open systems.

Conduction

is the direct transfer of energy from molecule to molecule through molecular collisions. As this definition would suggest, there must be direct physical contact between the objects. At the atomic level, the particles of the hotter matter transfer some of their kinetic energy to the particles of the cooler matter through collisions between the particles of the two materials. Metals are described as the best heat conductors because metallic bonds contain a density of atoms embedded in a sea of electrons, which facilitate rapid energy transfer. Gases tend to be the poorest heat conductors because there is so much space between individual molecules that energy-transferring collisions occur relatively infrequently. An example of heat transfer through conduction is the heat that is rapidly, and painfully, conducted to your fingers when you touch a hot stove.

Radiation

is the transfer of energy by electromagnetic waves. Unlike conduction and convection, radiation can transfer energy through a vacuum. Radiation is the method by which the Sun is able to warm the Earth. Most home kitchens have radiant ovens, which use either electrical coils or gas flames to heat the insulated metal box that forms the body of the oven. The hot metal box then radiates the energy through the open space of the oven, where it is absorbed by whatever food is placed inside.

Convection

is the transfer of heat by the physical motion of a fluid over a material. Because convection involves flow, only liquids and gases can transfer heat by this means. In convection, if the fluid has a higher temperature, it will transfer energy to the material. Most restaurants and some home kitchens have convection ovens, which use fans to circulate hot air inside the oven. Because the heat is being transferred to the food by both convection and radiation rather than only by radiation, convection ovens cook more rapidly than radiation-only ovens. Convection may also be used to wick heat away energy from a hot object. In laboratory experiments, for example, a running cold water bath may be used to rapidly cool a reaction.

When heat energy is added to or removed from a system, the temperature of that system will change in proportion to the amount of heat transfer, unless the system is undergoing a phase change during which the temperature is constant. This relationship between heat and temperature for a substance is called the specific heat. The specific heat (c) of a substance is defined as the amount of heat energy required to raise one gram of a substance by one degree Celsius or one unit kelvin. For example, the specific heat of liquid water is one calorie per gram per unit kelvin Equivalently, this can be expressed as The specific heat for a substance changes according to its phase. The MCAT will generally provide specific heat values as necessary, although you are expected to know the specific heat of water in calories. The equation that relates the heat gained or lost by an object and the change in temperature of that object is

q = mc Δ T where m is the mass, c is the specific heat of the substance, and ΔT is the change in temperature (in Celsius or kelvin). Because the unit size for the Celsius and Kelvin scales is the same, the change in temperature will be the same for temperatures measured in Celsius or kelvin.

The second law of thermodynamics

states that objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature at thermal equilibrium. As such, energy is constantly being dispersed.

The second law of thermodynamics states

that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. Pay attention to this: the usual way of thinking about entropy as "disorder" must not be taken too literally, a trap that many students fall into. Be very careful in thinking about entropy as disorder. The old analogy between a messy (disordered) room and entropy is deficient and may not only hinder understanding but actually increase confusion.

When heat energy is added to or removed from a system that is experiencing a phase change, the amount of heat that is added or removed cannot be calculated with the equation q = mc Δ T because there is no temperature change during a phase change. Instead, the following equation is used: q = mL

where q is the amount of heat gained or lost from the material, m is the mass of the substance, and L is the heat of transformation or latent heat of the substance.

Because the property of thermal expansion was integral to the development of thermometers, let's look a little more closely at this phenomenon. A change in the temperature of most solids results in a change in their length. Rising temperatures cause an increase in length, and falling temperatures cause a decrease in length. The amount of length change is proportional to the original length of the solid and the increase in temperature according to the equation ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature. The coefficient of linear expansion is a constant that characterizes how a specific material's length changes as the temperature changes. This usually has units of K , although it may sometimes be quoted as °C . This difference is inconsequential because the unit size for the Kelvin and Celsius scales is the same.

Entropy is the measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out, or how widely spread out energy becomes in a process. In the discussion of microstates earlier, we considered that when ice melts, the freedom of movement of the water molecules increases. If the water remains at the melting point, it will have the same average kinetic energy as molecules of ice; the difference between the two is the number of available microstates. That is, while both water and ice at 0°C have the same kinetic energy, the energy is dispersed over a larger number of microstates in liquid water. Liquid water therefore has higher entropy and, by extension, it is indeed less organized than ice. The equation for calculating the change in entropy is:

where ΔS is the change in entropy, Q is the heat that is gained or lost in a reversible process, and T is the temperature in kelvin. When energy is distributed into a system at a given temperature, its entropy increases. When energy is distributed out of a system at a given temperature, its entropy decreases. Notice that the second law states that energy will spontaneously disperse; it does not say that energy can never be localized or concentrated. However, the concentration of energy will rarely happen spontaneously in a closed system. Work usually must be done to concentrate energy. For example, refrigerators work against the direction of spontaneous heat flow (that is, they counteract the flow of heat from the "warm" exterior of the refrigerator to the "cool" interior), thereby "concentrating" energy outside of the system in the surroundings. As a result, refrigerators consume a lot of energy to accomplish this movement of energy against the temperature gradient.

Remember that in the absence of nonconservative forces, the sum of kinetic and potential energies is constant in a system. Now, in our present discussion of thermodynamics, we will look more closely at the relationship between internal energy, heat, and work. Essentially, the first law of thermodynamics states that the change in the total internal energy of a system is equal to the amount of energy transferred in the form of heat to the system, minus the amount of energy transferred from the system in the form of work. The internal energy of a system can be increased by adding heat, doing work on the system, or some combination of both processes. The change in internal energy is calculated from the equation ΔU = Q − W

where ΔU is the change in the system's internal energy, Q is the energy transferred into the system as heat, and W is the work done by the system.

Liquids also experience thermal expansion, but the only meaningful parameter of expansion is volume expansion. The formula for volumetric thermal expansion is applicable to both liquids and solids: ΔV = βVΔT

where ΔV is the change in volume, β is the coefficient of volumetric expansion, V is the original volume, and ΔT is the change in temperature. The coefficient of volumetric expansion is a constant that characterizes how a specific material's volume changes as the temperature changes. Its value is equal to three times the coefficient of linear expansion for the same material (β = 3α).