Chapter 2 | The First Law: Energy Is Conserved

Question 1

What is a scientific law?

Answer 1

A scientific law is a regularity observed in nature and formulated after many observations

-Emperical (info that is gained through observation, experience, experimentation, or direct sensory perception. Empirical data or findings are based on real-world observations and concrete evidence rather than being purely theoretical or speculative)
-Universal meaning they apply under a wide range of conditions and are not limited to specific situations or locations.
-repeated and consistent observations.
-Predictive: Laws are used to make predictions about future events or outcomes. They allow scientists to anticipate how a system will behave based on the law’s principles.
-Succinct and Mathematical: Scientific laws are often expressed in concise mathematical equations or statements that capture the essence of the relationship they describe.
it remains valid until new evidence arises that challenges or modifies it.

Question 2

What is thermodynamics? What is its relation to scientific law?

Answer 2

Thermodynamics is a branch of physics that deals with the study of energy and its transformations in physical systems. It provides a framework for understanding how heat and work relate to each other and how they affect the properties and behavior of matter.

The branch of science we call thermodynamics deals with the exchange of energy.
Scientific observations of how the exchange of energy happens ultimately lead to laws that
govern the direction of all natural processes.

Question 3

Even though chemistry is the study of matter, what effects matter?

Answer 3

Energy

Question 4

What is the first law of thermodynamics?

Answer 4

The First Law of Thermodynamics states that energy is conserved; that is, in any
process, energy can neither be created nor destroyed. it can simply be transferred from one place to another via heat and work.

Kind of like money

Question 5

Explain the transfer of heat and work into a system, 2 ways in which a system can increase its internal energy.

Answer 5

if a system gains heat it gains energy and this is known as the internal energy (U) of the system.
Surroundings can do work on a system

1. Transfer of heat energy into system
2. Surroundings performing work on a system

Question 6

What is energy?

Answer 6

Energy is anything that has the capacity to do work.
Energy can be exchanged between objects through contact like collisions for example

Question 7

What is Work?

Answer 7

Work is a force acting over a distance
Energy = work = force × distance (Mechanics Def.)

Question 8

What is Heat?

Answer 8

Heat is the flow of energy caused by a difference in temperature

Question 9

What did Einstein’s equation E=mc^2, reveal about the

Answer 9

E=mc^2
In everyday life, we don’t typically encounter situations where mass is being converted into energy or vice versa.
Nuclear Reactions and Radioactivity: The text points out that the conversion of mass into energy (or energy into mass) is primarily observed in extreme circumstances, specifically in nuclear reactions and radioactive processes. In these cases, the binding energy within atomic nuclei can be released, resulting in the conversion of a small amount of mass into a large amount of energy (as described by E=mc^2).

Question 10

How was the second law discovered?

Answer 10

the process of converting heat into work in these engines was not perfectly efficient. Some of the heat energy was lost or had to be discharged into a colder environment.
-This led to the formulation of the Second Law of Thermodynamics, which states that no heat engine, no matter how well-designed, can convert heat into work with perfect efficiency. In other words, there will always be some heat that is wasted or dispersed into a colder environment in order to drive the conversion of the rest into work.

-One important aspect of the Second Law is the observation that heat naturally flows from objects at higher temperatures to objects at lower temperatures. This concept is a fundamental part of the Second Law.

-The Second Law has broader implications beyond just heat engines. It dictates the direction of all spontaneous processes, not just the flow of heat. In essence, it tells us that certain processes in nature tend to occur in a particular direction because they lead to an increase in entropy (a measure of disorder) in the universe.
-Understanding the Second Law is incredibly useful because it helps us predict the natural direction of various processes. For example, it explains why ice melts when placed in a warmer environment or why a hot cup of coffee cools down over time.

Question 11

What concept is introduced in the 2nd law of thermodynamics?

Answer 11

The concept of entropy is introduced in the Second Law. Entropy is a measure of disorder or randomness in a system. It’s a quantity that tends to increase in any spontaneous process. In other words, as processes occur naturally, they often lead to an increase in entropy, which means systems become more disordered over time.

Heat naturally flows from Hot to Cold

amount of disorder or randomness in a system. It is often associated with the Second Law of Thermodynamics, which states that in a closed system, entropy tends to increase over time. This implies that natural processes tend to move towards a state of greater disorder.\
Example: room gets dirty no matter what, naturally gets messy, things get old, cars don’t appreciate
naturally things tend to go towards a disorderly state

Question 12

As heat flows from hot to cold, this is a?

Answer 12

spontaneous process
Where entropy increases always greater than 0

Question 13

What is the 3rd Law of thermodynamics?

Answer 13

When a system reaches absolute zero temperature or zero Kelvin, its entropy is defined to be zero, which means it is in a state of perfect order and complete absence of randomness.

biological systems never naturally reach temperatures anywhere close to absolute zero. In fact, biological systems typically operate at much higher temperatures. This is why the Third Law of Thermodynamics has limited relevance or practical application in the study of biological systems

the Third Law is important in the biological sciences because it provides an absolute measure of entropy.

Question 14

Why are the laws of thermodynamics important to understand and how are they relevant to understanding the world?

Question 15

What is Potential Energy?

Answer 15

Potential Energy:
Definition: Potential energy is the energy that an object possesses due to its position or configuration relative to other objects.
Examples:
Gravitational Potential Energy: An object raised above the ground has gravitational potential energy because it has the potential to fall and convert that energy into kinetic energy.
Elastic Potential Energy: When you stretch a rubber band or compress a spring, they store potential energy, which can be released when they return to their original shape.

Energy that is stored in a object or energy associated with the composition and position of the object

Question 16

What is Kinetic Energy?

Answer 16

Kinetic Energy:
Definition: Kinetic energy is the energy associated with the motion of an object. The faster an object moves and the more massive it is, the greater its kinetic energy.
Examples:
A moving car has kinetic energy because it is in motion.
A spinning top has kinetic energy due to its rotational motion.

Energy of motion or energy that is being transferred

Question 17

What is thermal energy?

Answer 17

The energy associated with temperature.
Thermal energy is a form or type of kinetic energy.

Question 18

What is Chemical energy?

Answer 18

Chemical energy is a type of potential energy.
-Associated with positions of electrons and nuclei

-Potential energy due to the structure of the atoms, the attachment between atoms, the atoms’ positions relative to each other in the molecule, or the molecules’ relative
positions in the structure

Question 19

Definitions of systems and surroundings?

Answer 19

• We define the system as the material or process within which we are studying the energy changes within.
• We define the surroundings as everything else with which the system can exchange energy.
• What we study is the exchange of energy between the system and the surroundings.
  SYSTEM
  – The object under study
  SURROUNDINGS
  – Everything outside the system
• Energy flows between the two

what separates the system from the surroundings is termed the boundary

Question 20

• Energy flows between these two

Answer 20

System and Surroundings

Question 21

Conservation of energy means that the amount of energy gained or lost by the system has to be?

Answer 21

equal to the amount of energy lost or gained by the surroundings.

Conservation of energy requires that the sum of the energy changes in the system and the surroundings must be zero.
∆Energyuniverse = 0 = ∆Energysystem + ∆Energysurroundings

Question 22

Thermodynamics deals with what three idealized kinds of system?

Answer 22

Open, closed, and Isolated systems.

In an open system, matter (such as chemicals) and energy (such as heat and light) can be exchanged or pass through the boundary between the system and surroundings. it can enter and leave the system

In a closed system, only energy aka heat is exchanged or can pass through the boundary. not insulated to heat

In an isolated system, nothing can pass through the boundary, no exchange of any kind no matter or energy. Nothing can enter or leave.

We must, however, always define the chosen system clearly, to avoid confusion.
it is entirely up to us to specify our system and to define
real or imaginary boundaries that separate it from its surroundings

Question 23

Which system is the most difficult to construct?

Answer 23

Isolated systems are the most difficult to construct, because it is hard to completely cut
off energy transfer to a system. However, the contents of a sealed and thermally insulated
f lask come very close to an isolated system, especially over a short period of time with negli-gible heat flow in and out.

Question 24

How can energy be exchanged between a system and its surroundings?

Answer 24

Energy exchange between a system and its surroundings can be divided into different types. Two of the most common types of energy exchange are work and heat. Work refers to the energy transfer due to mechanical processes, such as the expansion or compression of gases, while heat is the transfer of thermal energy between the system and its surroundings due to temperature differences.

Question 25

In classical mechanics, work is defined as?

Answer 25

The product of a force times a distance

Question 26

When is the work positive and negative?

Answer 26

Physical chemists and biochemists
generally follow the convention that the work is positive if the surroundings are doing
work on the system , and negative if the system is doing work on the surroundings .

Energy transfer into system is positive
Energy transfer into surroundings is negative
So
when we use Eq. w=f*d , we need to keep a watchful eye to make sure that the sign of work,
which depends on the proper choice of signs for the force and the displacement, is always
consistent with this convention.

Question 27

Difference between force and pressure?

Answer 27

Force:

Force is a vector quantity, meaning it has both magnitude (size or strength) and direction.
Force represents the push or pull applied to an object to change its motion, accelerate it, deform it, or change its state of rest.
The standard unit of force in the International System of Units (SI) is the newton (N).

Pressure is a concept related to force but is fundamentally different in its definition and application. Let’s clarify the difference between pressure and force:

Force:

Force is a vector quantity, meaning it has both magnitude (size or strength) and direction.
Force represents the push or pull applied to an object to change its motion, accelerate it, deform it, or change its state of rest.
The standard unit of force in the International System of Units (SI) is the newton (N).
Pressure:

Pressure is a scalar quantity, which means it has magnitude but no specific direction.
Pressure is defined as the force applied per unit area over a surface or on an object. Mathematically, pressure (P) is expressed as P = F/A, where “F” is the force applied, and “A” is the area over which the force is distributed.
Pressure measures the intensity of force distributed over an area. It tells us how much force is applied per unit of surface area.
The SI unit of pressure is the pascal (Pa),

In summary, pressure is a measure of how force is distributed over an area, and it provides information about the intensity of force at a particular point or on a particular surface. Force, on the other hand, represents the overall push or pull applied to an object and includes information about both its magnitude and direction.

Question 28

External Pressure equation?

Answer 28

External pressure (Pex) is related to the external force (Fex) applied to the movable wall or piston by the equation:

Pex = Fex/A,
or P=F/A

Where A is the cross-sectional area of the piston.

Question 29

Work equation that includes pressure? This work is often referred to as pressure-volume work or pV work.

Answer 29

Fexdx = -PexdV = W

Question 30

Work associated with a change in volume ion the system is often termed?

Answer 30

pressure-volume work or pV work

Question 31

The SI unit of pressure is?

Answer 31

Pascal or Pa

Question 32

The SI unit of volume is?

Answer 32

The cubic meter or m^3.
1 cubic meter is larger than most chemists use, so Liters (L) is commonly used instead. 1 L = 10^-3 M^3

Question 33

We use bars instead of pascals sometimes

Answer 33

1 bar= 10^5 Pa

Question 34

What is friction?

Answer 34

Friction, specifically kinetic friction, is a force that opposes the motion of an object when it is in contact with a solid, liquid, or gas. It acts to slow down or retard the motion.
Kinetic friction is approximately independent of the velocity (speed of motion) and the contact area but is proportional to the load or force pressing the two surfaces together.

Question 35

Conservative vs. Dissipative Processes:

Answer 35

In some physical processes, like extending a spring or compressing a piston, the work done on the system can be stored as potential energy. This potential energy can be later released as work when the system returns to its original state. Such processes are called “conservative processes.”
However, when it comes to frictional work, the energy is not stored as potential energy but is instead converted into heat. This heat energy is not easily converted back into work. Therefore, processes involving friction are considered “dissipative processes.”

regardless of whether a process is conservative or dissipative, the total energy in a closed system is always conserved. Energy is not created or destroyed; it merely changes forms.
In conservative processes, work is stored as potential energy, whereas in dissipative processes like friction, work is converted into heat.

Question 36

When two objects are in contact with each other, they tend to exchange energy until their temperatures become equal.
The hotter object loses energy and cools down, while the colder object gains energy and warms up.
This energy exchange due to temperature differences is called?

Answer 36

Heat transfer

Question 37

What is Heat?

Answer 37

Heat is a specific quantity of energy that flows between objects when there is a temperature difference.
It can be thought of as the energy that moves from hot objects to cold objects or vice versa.

the energy that passes through the system-surroundings boundaries because of a tempera-ture difference between the two

Question 38

The sign convention for heat?

Answer 38

Similar to work, heat has a sign convention. Heat is considered positive when it flows into a system, adding energy to it.
Conversely, heat is considered negative when it flows out of a system, taking energy away from it.

Question 39

What is heat capacity ?

Answer 39

Heat capacity (C) is a property of a material or system. It tells us how much heat is needed to change the temperature of that material by a certain amount (usually 1°C or 1 K).
In other words, it’s a measure of how “heat-sensitive” a substance is.

Question 40

What happens when a closed system receives a small amount of heat (dq)?

Answer 40

Its temperature changes by a small amount (dT).

Question 41

Two equations to calculate heat capacity

Answer 41

The equation dq/dT = C
(or dq = C dT) quantifies how much heat is needed to change the temperature of the system.

Question 42

How to calculate total heat transfer?

Answer 42

To calculate the total heat (q) gained or lost when the temperature of the system changes from an initial temperature (T₁) to a final temperature (T₂), you can use the integral ∫C dT.
If the heat capacity (C) is constant over the temperature range, it can be factored out of the integral, and the calculation simplifies to q = C(T₂ - T₁)

Question 43

Extensive and Intensive Properties:

Answer 43

Extensive properties, like heat capacity, depend on the amount of material present and increase as the amount increases.

Intensive properties, like temperature and pressure, remain unchanged when a system is divided or subdivided and do not depend on the quantity of material.

Question 44

How can we convert C into an intensive quality? (one that depends only on the properties of the
substance, and not its amount)

Answer 44

To make heat capacity an intensive property, it can be divided by the number of moles of substance present, resulting in the molar heat capacity (Cm).

Question 45

heat capacity vs molar heat capacity?

Answer 45

Molar heat capacity (Cm) is a version of heat capacity that considers the heat energy required to change the temperature of one mole of a substance by 1 degree Celsius (1°C) or 1 Kelvin (1 K).
The SI unit of molar heat capacity is joules per mole per Kelvin (J mol⁻¹ K⁻¹).

Question 46

The SI unit of heat capacity and molar heat capacity?

Answer 46

The SI unit of heat capacity is joules per Kelvin (J K⁻¹), and the unit of molar heat capacity is J mol⁻¹ K⁻¹.

Question 47

What is specific heat capacity?

Answer 47

Specific heat capacity (often denoted as “c” in lowercase) is a related concept. It is the heat capacity divided by the mass of the substance.
The formula for specific heat capacity is c = C / m, where “C” is the heat capacity, and “m” is the mass of the substance.
The SI unit of specific heat capacity is joules per kilogram per Kelvin (J kg⁻¹ K⁻¹). However, it is sometimes given in joules per gram per Kelvin (J g⁻¹ K⁻¹).

Question 48

What explains the behavior of gases based on the motion of their constituent particles (atoms or molecules)?

Answer 48

Kinetic Theory of Gases: The kinetic theory of gases is a fundamental part of statistical mechanics It provides insights into the properties of ideal gases, which are theoretical gases that follow the ideal gas equation of state (pV = nRT) under certain conditions.

Question 49

What are the two key premises of the kinetic theory of gases?

Answer 49

Gases are composed of molecules that are in constant, random motion. These molecules collide with each other and with the walls of the container.
In the kinetic theory, gases are assumed to have no attractive forces between their molecules, and the collisions between molecules are considered perfectly elastic, meaning there is no net gain or loss of energy during collisions.

Question 50

the kinetic theory of gases equation?

Answer 50

p= (mN/3V) ⟨v^2⟩
significant because it connects the microscopic behavior of gas molecules (their velocities) to the macroscopic property of pressure. It helps us understand why gases exhibit certain properties and behaviors under different conditions.

Question 51

molar internal energy (Um) equation

Answer 51

1/2M(v^2)

Question 52

The key point here is that the internal energy of an ideal gas (
U
m
U
m
​
or
U
U) depends solely on temperature (
T
T). It’s independent of volume (
V
V) and pressure (
p
p). This makes sense because in the kinetic theory of ideal gases, it’s assumed that gas molecules don’t interact with each other. Therefore, changing the distance between them (volume) or the force they exert on the container walls (pressure) doesn’t affect their total kinetic energy.

Question 53

In classical thermodynamics, we express the
First Law by the equation..?

Answer 53

deltaU=w+q

Question 54

there are two ways we can add energy to a system; we can heat it, or do work on
it.
doing work requires
changing what?

Answer 54

As long as we keep the volume fixed, we do no work:

doing work requires
changing the volume.
Therefore, at constant volume,
U=qV.

Question 55

At constant volume what is the equation?

Answer 55

dU=qv

Question 56

What is internal energy?

Answer 56

The sum of the kinetic and potential energies of all the particles that compose the system. Internal energy is a state function.

delta U=E final/products-E initial/reactants

Question 57

What does the change in internal energy of a system depend on?

Answer 57

It depends only on the amount of energy in the system at the beginning and end

Question 57

What is a state function?

Answer 57

A mathematical function whose result only depends on the initial and final conditions, not on the process used or the path used to accomplish it.

Question 58

What does the equation Cv=3/2R mean? CV/R=3/2

Answer 58

This equation indicates that the heat capacity of all ideal gases (when considering their molar heat capacity) should be the same.

Question 58

Why do the molar heat capacities of atoms in crystal lattices differ from those in ideal gases?

Answer 58

The key difference is that atoms in a crystal lattice interact with their neighboring atoms, leading to potential energy. In contrast, atoms in an ideal gas do not interact and have no potential energy. This interaction in the lattice allows atoms to store some of their internal energy as potential energy.

In a crystal lattice, an atom can put RT/2 units of internal energy into kinetic energy and RT/2 units into potential energy along a particular direction, doubling its total internal energy compared to the same atom in an ideal gas at the same temperature.

The passage also mentions that vibrational modes in a crystal lattice always have both kinetic and potential energy components, allowing them to absorb RT units of energy per mode. In contrast, rotational modes in an ideal gas can only absorb RT/2 units because there is no associated potential energy with rotation.

Question 58

What factors effect the heat capacities of molecular solids and liquids?

Answer 58

*
Factors Affecting Heat Capacity
The heat capacity of an object depends on its amount of matter.
– It is usually measured by its mass.
– 200 g of water requires twice as much heat to raise its
temperature by 1 °C as does 100 g of water.
The heat capacity of an object depends on the type of
material.
– 1000 J of heat energy will raise the temperature of 100 g of sand 12 °C, but only raise the temperature of 100 g of water by 2.4 °C

temperature, molecular structure, and molecular mass

The molar heat capacities tend to increase with molecular mass (M) because larger molecules have more atoms, leading to more low-energy vibrations that can absorb heat. The passage implies that as you move down the rows in the table, molecules with similar mass but more flexibility have higher heat capacities than those composed of rigid molecules.

Question 59

Why does water have a higher heat capacity at its melting point than ice?

Answer 59

liquids generally have higher heat capacities at their melting points compared to the corresponding solids.

Question 59

What are the two types of variables used in thermodynamics?

Answer 59

state variables and path variables

Question 59

What are state variables? List them.

Answer 59

State variables are properties of a system that depend only on its current state, not on how it reached that state.

is a mathematical function whose result only depends on the initial and final conditions, not on the
process used or the path used to accomplish it.

In the context of a closed system, specifying certain state variables like pressure (p), volume (V), and temperature (T) for a pure liquid is sufficient to determine many other properties of the liquid, such as density, surface tension, and refractive index.
State variables are useful because when you specify a few of them, all other properties of the system become implicitly determined.
Examples of state variables include p, V, T, and chemical composition.

Question 60

What are path variables? List them.

Answer 60

Path variables are properties of a system that depend on the specific path or process by which the system reached its current state.

Heat (q) and work (w) are examples of path variables. These quantities can vary depending on how energy is transferred to or from the system and the path taken.

Question 61

Path to State Conversion

Answer 61

When you specify the path taken during a process, certain path variables can become state variables.
For instance, the heat capacity (C) is a path variable (dq/dT) because it depends on the specific process (q). However, if you specify a constant volume path, the heat capacity at constant volume (CV) becomes a state variable and is equal to the rate of change of internal energy with respect to temperature (dU/dT).

Question 62

volume of a solid or liquid is ?

Answer 62

remains constant and is denoted as V₀ (volume under standard conditions, typically 298 K and 1 bar).
This means that calculating the volume of a solid or
liquid simply requires finding the density or specific volume at one temperature and using
that value for any temperature and pressure. The volume is related to the density by V=m/p

Question 63

The volume of a gas is?

Answer 63

an change significantly with changes in temperature (T) and pressure (p), but it is nearly independent of the type of gas.

Question 64

The simplest approximate equation of state for gases is the ?

Answer 64

Ideal Gas Law, which is represented as pV = nRT, where:
p is the pressure
V is the volume
n is the number of moles of the gas
R is the gas constant
T is the temperature