Chapter 3: Thermodynamics

calorie (cal), 4184, British thermal unit (BTU)

Fill in the conversion factors between the units of heat. 1 nutritional Calorie (Cal) = 10³ ______ = ______ joules (J) = 3.97 ______

Conduction

There are three means by which heat can transfer energy. ______ is the direct transfer of energy from molecule to molecule through molecular collisions.

State (These type of 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.)

______ functions are pathway independent and are not themselves defined by a process.

Process

______ functions describe the pathway from one equilibrium state to another.

Closed

______ systems exchange energy but not matter with their surroundings.

decrease

A change in the temperature of most solids results in a change in their length. Falling temperatures cause a(n) (DECREASE / INCREASE) in length.

210 kJ, 90 kJ (The pressure is held constant through the entire process so the work can be found using the equation: W=P∆V = (3.5 x 10⁵ Pa)(1.5 m³ - 0.9 m³) = 2.1 x 10⁵ J. The change in internal energy can be found from the first law of thermodynamics: ∆U = Q-W = (3.5 x 10⁵ J) - (2.1 x 10⁵ J) = 0.9 x 10⁵ J = 90 kJ.)

A gas in a cylinder is kept at a constant pressure of 3.5 x 10⁵ Pa while 300 kJ of heat are added to it, causing the gas to expand from 0.9 m³ to 1.5 m³. Find the work done by the gas and the change in internal energy of the gas.

1.998 m (Substitute directly into the thermal expansion formula: ΔL = αLΔT = (10^-6 K)(2 m)(80 K - 1080 K) = -2 x 10^-3 m. The negative sign represent a decrease in length. The original length was 2 m; therefore; the final length is 2-(2x10^-3) = 1.998 m.)

A metal rod of length 2 m has a coefficient of linear expansion of 10^-6 K^-1. It is cooled from 1080°C to 80°C. What is the final length of the rod?

a lot (αLΔT)

A mnemonic for the thermal expansion equation is: when the temperature of an object changes, its length changes ______ ______.

A (Calorimeters are our best approximations of isolated systems, where neither energy nor matter is exchanged with the environment. By failing to use an insulating layer and failing to fully contain the system, heat can be exchanged with the environment and matter may be dispersed, creating an open system.)

A student making a coffee cup calorimeter fails to use a second coffee cup and inadequately seals the lid. What was her initial goal, and what was the result of this mistake? A.) She was trying to create an isolated system but created an open system instead. B.) She was trying to create an isolated system but created a closed system instead. C.) She was trying to create a closed system but created an open system instead. D.) She was trying to create a closed system but created an isolated system instead.

A (To find the amount of heat needed to bring the substance to its melting point, you can use the specific heat. To heat one mole of the substance one unit kelvin, it would take 1 J of heat. After the substance reaches its melting point, additional heat is needed to actually induce the phase change. Therefore, the total amount of heat required is greater than 1 J.)

A substance has a specific heat of 1 J/mol∙K and a melting point of 350 K. If one mole of the substance is currently at a temperature of 349 K, how much energy must be added in order to melt it? A.) More than 1 J B.) Exactly 1 J C.) Less than 1 J but more than 0 J D.) Less than 0 J

system, surroundings

A thermodynamic ______is the portion of the universe that we are interested in observing, whereas the rest of the universe is considered the ______.

-273

Absolute zero in Celsius.

-460

Absolute zero in Fahrenheit.

0

Absolute zero in Kelvin.

conduction

At the atomic level, ______ refers to particles of the hotter matter transferring some of their kinetic energy to the particles of the cooler matter through collisions between the particles of the two materials.

100

Boiling point of water in Celsius.

212

Boiling point of water in Fahrenheit.

373

Boiling point of water in Kelvin.

A (Heat Q is positive when heat flows into the system and negative when heat flows out.)

Choose the appropriate sign convention for Q in the equation ΔU = Q - W if heat flows into the system. A.) Positive value B.) Negative value

B (When work is done by the system (expansion), W is positive. When work is done on the system (compression), W is negative.)

Choose the appropriate sign convention for W in the equation ΔU = Q - W if work is done on the system. A.) Positive value B.) Negative value

B (The change in internal energy ΔU is positive with increasing temperature and negative with decreasing temperature.)

Choose the appropriate sign convention for the change in internal energy (ΔU) in the equation ΔU = Q - W if the temperature is decreasing. A.) Positive value B.) Negative value

potential, kinetic, heat of transformation

During a phase change, heat energy causes changes in the particles' ______ energy and energy distribution (entropy), but NOT ______ energy. Therefore, there is no change in temperature. This is the ______ ______ ______.

isothermal, change in internal energy, Q=W (∆U=0)

For ______ processes (dark purple trend), the temperature is constant, and the ______ is therefore 0. This reduces the first law of thermodynamics to ______. NOTE blanks may contain more than one word.

isobaric

For ______ processes (green trend), the pressure is held constant.

isochoric (also accept isovolumetric), work, deltaU=Q (W=0)

For ______ processes (light purple trend), the volume is held constant and the ______ is therefore 0. This reduces the first law of thermodynamics to ______. NOTE blanks may contain more than one word.

adiabatic, deltaU = -W (Q=0)

For ______ processes (yellow trend), no heat is exchanged. This reduces the first law of thermodynamics to ______.

0

Freezing point of water in Celsius.

32

Freezing point of water in Fahrenheit.

273

Freezing point of water in Kelvin.

thermal equilibrium

Heat is the process of energy transfer between two objects at different temperatures that occurs until the two objects come into ______ ______ (reach the same temperature).

30, 303 (To convert from Fahrenheit to Celsius use the equation: F = 5/9(86-32) = 5/9(54) = 30°C. To convert to Kelvin add 273 to the Celsius value.)

If a meteorologist says that the temperature will reach a high of 86°F today, what will be the high temperature in °C and in K?

245 J/K (We know that during a phase change, the temperature is constant; in this case, 273 K. The equation for calculating the change in entropy is: ∆S = Qrev/T where ∆S is the change in entropy, Qrev is the heat that is gained or lost in a reversible process, and T is the temperature in kelvin. From the information given, ∆S = Qrev/T = 6.66 x 10⁴ J / 272 K = 245 J/K.)

If, in a reversible process, 6.66 x 10⁴ J of heat is used to change a 200 g block of ice to water at a temperature of 272 K, what is the change in the entropy of the system? (Note: the heat of fusion of ice = 333 J/g.)

closed-loop

In a(n) ______-______ process, like that depicted in the figure, the system returns to its original thermodynamic state of temperature and pressure, and the shaded area of a P-V diagram is equal to work.

B (An adiabatic process means that there is no exchange of heat; in other words Q=0. When a gas is compressed, positive word is being done ON the gas (rather than BY the gas), so the value for work done by the gas will be negative (W<0). Based on this, we can determine how the internal energy of the gas changes by using the first law of thermodynamics (∆U=Q-W). If Q=0 and W is negative, then ∆U is positive.)

In an adiabatic compression process, the internal energy of the gas: A.) increases because the work done on the gas is negative. B.) increases because the work done on the gas is positive. C.) decreases because the work done on the gas is negative. D.) decreases because the work done on the gas is positive.

B (When the ink randomly intersperses throughout the water, the final state is more disordered than the initial state, so the entropy change of the system is positive. When the oil separates from the water, the final state is just as ordered as the initial state (because the oil and the water are still completely separate), so the entropy change is zero. You can also answer this question by noticing the reversibility of the two experiments. Experiment A has a positive entropy change because it is irreversible, while experiment B has no entropy change because the reaction is reversible. According to the second law of thermodynamics, the overall entropy change of a system and its surroundings can never be negative in a thermodynamic process that moves from one equilibrium state to another.)

In experiment A, a student mixes ink with water and notices that the two liquids mix evenly. In experiment B, the student mixes oil with water; in this case, the liquids separate into two different layers. The entropy changes is: A.) positive in experiment A and negative in experiment B. B.) positive in experiment A and zero in experiment B. C.) negative in experiment A and positive in experiment B. D.) zero in experiment A and negative in experiment B.

coefficient of volumetric expansion

Liquids also experience thermal expansion, but the only meaningful parameter of expansion is volume expansion and is described by the equation: ΔV = βVΔT, where ΔV is the change in volume, β is the ______ ______ ______ ______ (a constant that characterizes how a specific material's volume changes as temperature changes), and ΔT is the change in temperature.

microstates

On a statistical level, as the number of available ______ increases, the potential energy is more greatly dispersed, increasing entropy.

325 kJ (Before melting the chain, we must first heat the chain to the melting point. To figure out how much heat is required, we use the formula: q = mc∆T = (1 kg)(233 J/kg∙K)(962-942) = 2.19 x 10⁵ J. This tells use we have to add 219 kJ of heat to the chain just to get its temperature to the melting point. The chain is still in the solid phase. To melt it, we must continue to add heat in accordance with the formula q = mL = (1 kg)(1.05 x x 10⁵ J/kg) = 1.05 x 10⁵ J. The total heat needed to melt the solid silver chain is 220 kJ + 105 kJ = 325 kJ.)

Silver has a melting point of 962°C and a heat of fusion of approximately 1.05 x 10⁵ J/kg. The specific heat of silver is 233 J/kg∙K. Approximately how much heat is required to completely melt a 1 kg silver chain with an initial temperature of 20°C?

D (Saying that substance B has a higher internal energy cannot explain the phenomenon because the internal energy is irrelevant; the heat involved in the process is related only to the specific heat, the heat of fusion, and the heat of vaporization. All of the other choices could explain this phenomenon. The heat required to melt the solid is determined by the heat of fusion, choice C. The heat required to bring the liquid to its boiling point is determined by the specific heat, choice A. The heat required to boil the liquid is determined by the heat of vaporization, choice B.)

Substances A and B have the same freezing and boiling points. If solid samples of both substances are heated in the exact same way, substance A boils before substance B. Which of the following would NOT explain this phenomenon? A.) Substance B has a higher specific heat. B.) Substance B has a higher heat of vaporization. C.) Substance B has a higher heat of fusion. D.) Substance B has a higher internal energy.

0.045 mL (Use the information to plug into the volumetric expansion formula: ΔV = βVΔT = (1.8 x 10^-4 K^-1)(1 mL)(225°C-(-25°C)) = (1.8 x 10^-4)(250) = 450 x 10^-4 mL = 0.045 mL.)

Suppose that a thermometer with 1 mL of mercury is taken from a freezer with a temperature of -25°C and placed near an oven at 225°C. If the coefficient of volume expansion of mercury is 1.8 x 10^-4 K^-1, by how much will the liquid expand?

coefficient of linear expansion

The amount of length change in a solid due to rising or falling temperatures is proportional to the original length of the solid according to the following equation: ΔL = αLΔT, where ΔL is the change in length, α is the ______ ______ ______ ______ (constant that characterizes how a specific material's length changes as the temperature changes with units of K^-1), L is the original length, and ΔT is the change in temperature.

three (β = 3α)

The coefficient of volumetric expansion (β) is equal to ______ times the coefficient of linear expansion for the same material (α).

C (In this situation, heat will transfer from the warm gas to the metal and then to the cold gas. Choice B, convection, requires flow of a fluid to cause heat transfer. In this case, the gas is not flowing, but rather is in contact with the metal. Choice A, heat transfer through radiation, is also implausible not only because gases are unlikely to emit heat in the form of waves, but also because the radiation would be unlikely to penetrate the thick metal container. Enthalpy, choice D, is not a form of heat transfer. Conduction, choice C, is the most likely option; it happens when two substances make direct contact with one another. Here gas A makes contact with the metal container, which makes contact with gas B.)

The figure shown depicts a thick metal container with two compartments. Compartment A is full of a hot gas, while compartment B is full of a cold gas. What is the primary mode of heat transfer in this system? A.) Radiation B.) Convection C.) Conduction D.) Enthalpy

evaporation (also accept boiling or vaporization), condensation, heat of vaporization

The phase change from liquid to gas (_______) or gas to liquid (______) occurs at the boiling point. The corresponding heat of transformation (L) is called the _______ ______ _______.

freezing (also accept solidification), melting (also accept fusion), heat of fusion

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

B (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: ∆Suniverse = ∆Ssystem +∆Ssurroundings > 0.)

The universe is a closed, expanding system, so the entropy of the universe is always _______. A.) decreasing B.) increasing C.) constant D.) changing

Radiation

There are three means by which heat can transfer energy. ______ is the transfer of energy by electromagnetic waves.

Convection

There are three means by which heat can transfer energy. ______ is the transfer of heat by the physical motion of a fluid over a material.

False (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.)

True or False: Convection occurs in all states of matter.

True (It 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.)

True or False: Differences in temperature determine the direction of heat transfer.

False (Every natural process is ultimately IRREVERSIBLE; under highly controlled conditions, certain equilibrium processes such as phase changes can be treated as essentially reversible.)

True or False: Every natural process is ultimately reversible.

False (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.)

True or False: Objects do not necessarily have to be touching for conduction to occur.

True (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 objects are also in thermal equilibrium. As such, when brought into thermal contact, no net heat will flow between these objects. In a more general form, if a = b and b = c, then a = c.)

True or False: Objects in thermal equilibrium experience no net exchange of heat energy.

False (Phase changes are related to changes in potential energy, not kinetic energy. When heat is added to ice, the heat energy causes water molecules to break free of the hydrogen bonds between them. This increased freedom of movement permits a greater number of microstates and a greater potential energy. For example, instead of only being able to move up and down or sway side-to-side, a water molecule may now be able to rock forward and back. In gaining additional 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.)

True or False: Phase changes are related to changes in kinetic energy.

True (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. This constancy in temperature is the heat of transformation.)

True or False: 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.

True (State functions are independent of the path taken to get to a particular equilibrium state and are thus a function of only the current equilibrium state of a system.)

True or False: Pressure (P), density (ρ), temperature (T), volume (V), enthalpy (H), internal energy (U), Gibbs free energy (G), and entropy (S) are all state functions.

False (Accuracy is related to an instrument, rather than the scale. In addition, Kelvin uses the same scale as Celsius, so there are no practical differences in terms of accuracy.)

True or False: The Kelvin scale is the most accurate measurement method for temperature because it is based on absolute zero.

True (Although the second law states that energy will spontaneously disperse, it does not say that energy can never be localized or concentrated. Work usually must be done to concentrate energy. As an example, refrigerators work against the direction of spontaneous heat flow, thereby "concentrating" energy outside of the system in the surroundings.)

True or False: The concentration of energy will not happen spontaneously in a closed system.

True (Isolated systems are not capable of exchanging energy or matter with their surroundings. Since there are no surroundings outside the entire universe, it can be considered an isolated system.)

True or False: The entire universe can be considered an isolated system.

False (The specific heat, or the amount of heat energy required to raise one gram of a substance by one degree Celsius or one unit kelvin, changes according to a substance's phase.)

True or False: The specific heat is constant for a given substance across phase changes.

True (The Kelvin scale starts from absolute zero, or the theoretical temperature at which there is no thermal energy.)

True or False: There are no negative temperatures on the Kelvin scale.

False (Thermal contact does not necessarily imply physical contact, as objects can be in thermal contact across space.)

True or False: Thermal contact requires physical contact between objects.

True (Radiation is the transfer of energy by electromagnetic waves. It is the method by which the Sun is able to warm the Earth.)

True or False: Unlike conduction and convection, radiation can transfer energy through a vacuum.

False (An exception occurs if the system is undergoing a phase change during which the temperature is constant. Otherwise, when heat is added to or removed from a system, the temperature change is proportional to the amount of heat transfer - a relationship defined by the specific heat of a substance.)

True or False: When heat energy is added to or removed from a system, the temperature of the system will always change in proportion to the amount of heat transfer.

False (Work and heat are process functions because they describe the path taken to get from one equilibrium state to another.)

True or False: Work and heat are state functions.

False (An adiabatic process refers to one in which no heat is exchanged. This makes Q=0 and ∆U=-W. The relationship ∆U=Q is true for an isochoric process in which the volume is kept constant making W=0.)

True or False: ∆U=Q for an adiabatic process.

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; NOTE: q=mcΔT cannot be used in this case because there is no temperature change during a phase change.)

What equation is used to calculate the amount of heat added or removed from a system that is experiencing a phase change?

q=mcdeltaT (where m is the mass, c is the specific heat of the substance, and ΔT is the change in temperature)

What equation relates the heat gained or lost by an object to the change in temperature of that object?

F=9/5C+32

What formula can be used to convert from Celsius to Fahrenheit?

K=C+273

What formula can be used to convert from Celsius to Kelvin?

joule (J, Heat is a type of energy.)

What is the SI unit for heat?

specific heat (c)

What is the amount of energy necessary to raise one gram of a substance by one degree Celsius or one unit kelvin?

C (To answer this question, first remember that watts are equal to joules per second; in other words, power is energy transfer over time. In 10 minutes, the pendant absorbs the following amount of energy: E = P x t = (100 W)(10 min)(60 s/1 min) = 6 x 10⁴ J. Now we can find the final temperature from this equation: q = mc∆T. 6 x 10⁴ J = (5 kg)(233 J/kg∙K)∆T, ∆T = 52°C. The final temperature is thus 20 + 52 = 72°C.)

What is the final temperature of a 5 kg silver pendant that is left in front of an electric heat, absorbing heat energy at a rate of 100 W for 10 minutes? Assume the pendant is initially at 20°C and the specific heat of silver is 233 J/kg*K. A.) 29°C B.) 59°C C.) 72°C D.) 100°C

1 cal/g*K(= 4.184 J/g∙K; Remember specific heat is the amount of energy necessary to raise one gram of substance by one unit kelvin.)

What is the specific heat of liquid water in calories? NOTE: This is a constant you are expected to know for test day.

second law of thermodynamics (law of entropy)

What law states that in a closed system (up to and including the entire universe), energy will spontaneously and irreversibly go from being localized to being spread out (dispersed)?

zeroth law of thermodynamics

What law states that objects are in thermal equilibrium when they are at the same temperature?

first law of thermodynamics (This is a derivative of the law of conservation of energy which states that the total energy in the universe can never decrease or increase.)

What law states that the change in the total internal energy (ΔU) of a system is equal to the amount of energy transferred in the form of heat (Q) to the system, minus the amount of energy transferred from the system in the form of work (W)?

third law of thermodynamics

What law states that the entropy of a perfectly-organized crystal at absolute zero is zero?

B (Closed systems are capable of exchanging energy but not matter - so in this case the gas. For thermodynamic purposes, most of what will be encountered on the MCAT will be a closed system or will approximate a closed system.)

What type of system describes a gas in a vessel with a moveable piston? A.) Isolated B.) Closed C.) Open D.) Standard

thermal expansion (They allow for a change in length without damaging integrity.)

Why do bridges and sidewalks have gaps between their segments?

liquid (The potential energy in the solid is quite low because of the stability provided by the relative closeness of one molecule to another and by the hydrogen bonds. As water molecules are held less rigidly in place, they have greater degrees of freedom of movement and their average potential energy (and entropy) increases.)

Would you expect water to have a greater potential energy in the solid or liquid phase?

Thermal expansion

______ ______ describes how a substance changes in length of volume as a function of the change in temperature.

Metals

______ are described as the best conductors because these bonds contain a density of atoms embedded in a sea of electrons, which facilitate rapid energy transfer.

Temperature

______ is a quantity related to the average kinetic energy of the particles that make up a substance; qualitatively, it is a measure of how hot or cold an object is.

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.

Heat

______ refers to the transfer of thermal energy from a hotter object with higher temperature (energy) to a colder object with lower temperature (energy).

Isolated

______ systems do not exchange matter or energy with the surroundings. As a result, the total change in internal energy must be zero.

Open

______ systems exchange both energy and matter with their surroundings; not only does the matter carry energy, but more may be transferred in the form of heat or work.

Gases

______ tend to be the poorest heat conductors because there is so much space between individual molecules that energy-transferring collisions occur relatively infrequently.