• 12.3 Second Law of Thermodynamics: Entropy
  • Introduction
  • 1.1 Physics: Definitions and Applications
  • 1.2 The Scientific Methods
  • 1.3 The Language of Physics: Physical Quantities and Units
  • Section Summary
  • Key Equations
  • Concept Items
  • Critical Thinking Items
  • Performance Task
  • Multiple Choice
  • Short Answer
  • Extended Response
  • 2.1 Relative Motion, Distance, and Displacement
  • 2.2 Speed and Velocity
  • 2.3 Position vs. Time Graphs
  • 2.4 Velocity vs. Time Graphs
  • 3.1 Acceleration
  • 3.2 Representing Acceleration with Equations and Graphs
  • 4.2 Newton's First Law of Motion: Inertia
  • 4.3 Newton's Second Law of Motion
  • 4.4 Newton's Third Law of Motion
  • 5.1 Vector Addition and Subtraction: Graphical Methods
  • 5.2 Vector Addition and Subtraction: Analytical Methods
  • 5.3 Projectile Motion
  • 5.4 Inclined Planes
  • 5.5 Simple Harmonic Motion
  • 6.1 Angle of Rotation and Angular Velocity
  • 6.2 Uniform Circular Motion
  • 6.3 Rotational Motion
  • 7.1 Kepler's Laws of Planetary Motion
  • 7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity
  • 8.1 Linear Momentum, Force, and Impulse
  • 8.2 Conservation of Momentum
  • 8.3 Elastic and Inelastic Collisions
  • 9.1 Work, Power, and the Work–Energy Theorem
  • 9.2 Mechanical Energy and Conservation of Energy
  • 9.3 Simple Machines
  • 10.1 Postulates of Special Relativity
  • 10.2 Consequences of Special Relativity
  • 11.1 Temperature and Thermal Energy
  • 11.2 Heat, Specific Heat, and Heat Transfer
  • 11.3 Phase Change and Latent Heat
  • 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium
  • 12.2 First law of Thermodynamics: Thermal Energy and Work
  • 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators
  • 13.1 Types of Waves
  • 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period
  • 13.3 Wave Interaction: Superposition and Interference
  • 14.1 Speed of Sound, Frequency, and Wavelength
  • 14.2 Sound Intensity and Sound Level
  • 14.3 Doppler Effect and Sonic Booms
  • 14.4 Sound Interference and Resonance
  • 15.1 The Electromagnetic Spectrum
  • 15.2 The Behavior of Electromagnetic Radiation
  • 16.1 Reflection
  • 16.2 Refraction
  • 16.3 Lenses
  • 17.1 Understanding Diffraction and Interference
  • 17.2 Applications of Diffraction, Interference, and Coherence
  • 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge
  • 18.2 Coulomb's law
  • 18.3 Electric Field
  • 18.4 Electric Potential
  • 18.5 Capacitors and Dielectrics
  • 19.1 Ohm's law
  • 19.2 Series Circuits
  • 19.3 Parallel Circuits
  • 19.4 Electric Power
  • 20.1 Magnetic Fields, Field Lines, and Force
  • 20.2 Motors, Generators, and Transformers
  • 20.3 Electromagnetic Induction
  • 21.1 Planck and Quantum Nature of Light
  • 21.2 Einstein and the Photoelectric Effect
  • 21.3 The Dual Nature of Light
  • 22.1 The Structure of the Atom
  • 22.2 Nuclear Forces and Radioactivity
  • 22.3 Half Life and Radiometric Dating
  • 22.4 Nuclear Fission and Fusion
  • 22.5 Medical Applications of Radioactivity: Diagnostic Imaging and Radiation
  • 23.1 The Four Fundamental Forces
  • 23.2 Quarks
  • 23.3 The Unification of Forces
  • A | Reference Tables

Section Learning Objectives

By the end of this section, you will be able to do the following:

  • Describe entropy
  • Describe the second law of thermodynamics
  • Solve problems involving the second law of thermodynamics

Teacher Support

The learning objectives in this section will help your students master the following standards:

  • (G) analyze and explain everyday examples that illustrate the laws of thermodynamics, including the law of conservation of energy and the law of entropy

Section Key Terms

[BL] [OL] [AL] Review heat and absolute temperature. Recall earlier discussions on engine efficiency. Assess students' understanding of efficiency.

Recall from the chapter introduction that it is not even theoretically possible for engines to be 100 percent efficient. This phenomenon is explained by the second law of thermodynamics , which relies on a concept known as entropy . Entropy is a measure of the disorder of a system. Entropy also describes how much energy is not available to do work. The more disordered a system and higher the entropy, the less of a system's energy is available to do work.

The meaning of entropy is difficult to grasp, as it may seem like an abstract concept. However, we see examples of entropy in our everyday lives. For instance, if a car tire is punctured, air disperses in all directions. When water in a dish is set on a counter, it eventually evaporates, the individual molecules spreading out in the surrounding air. When a hot object is placed in the room, it quickly spreads heat energy in all directions. Entropy can be thought of as a measure of the dispersal of energy. It measures how much energy has been dispersed in a process. The flow of any energy is always from high to low. Hence, entropy always tends to increase.

Although all forms of energy can be used to do work, it is not possible to use the entire available energy for work. Consequently, not all energy transferred by heat can be converted into work, and some of it is lost in the form of waste heat—that is, heat that does not go toward doing work. The unavailability of energy is important in thermodynamics; in fact, the field originated from efforts to convert heat to work, as is done by engines.

The equation for the change in entropy, Δ S Δ S , is

where Q is the heat that transfers energy during a process, and T is the absolute temperature at which the process takes place.

Q is positive for energy transferred into the system by heat and negative for energy transferred out of the system by heat. In SI, entropy is expressed in units of joules per kelvin (J/K). If temperature changes during the process, then it is usually a good approximation (for small changes in temperature) to take T to be the average temperature in order to avoid trickier math (calculus).

Tips For Success

Absolute temperature is the temperature measured in Kelvins. The Kelvin scale is an absolute temperature scale that is measured in terms of the number of degrees above absolute zero. All temperatures are therefore positive. Using temperatures from another, nonabsolute scale, such as Fahrenheit or Celsius, will give the wrong answer.

Second Law of Thermodynamics

Have you ever played the card game 52 pickup? If so, you have been on the receiving end of a practical joke and, in the process, learned a valuable lesson about the nature of the universe as described by the second law of thermodynamics. In the game of 52 pickup, the prankster tosses an entire deck of playing cards onto the floor, and you get to pick them up. In the process of picking up the cards, you may have noticed that the amount of work required to restore the cards to an orderly state in the deck is much greater than the amount of work required to toss the cards and create the disorder.

The second law of thermodynamics states that the total entropy of a system either increases or remains constant in any spontaneous process; it never decreases. An important implication of this law is that heat transfers energy spontaneously from higher- to lower-temperature objects, but never spontaneously in the reverse direction. This is because entropy increases for heat transfer of energy from hot to cold ( Figure 12.9 ). Because the change in entropy is Q / T , there is a larger change in Δ S Δ S at lower temperatures (smaller T ). The decrease in entropy of the hot (larger T ) object is therefore less than the increase in entropy of the cold (smaller T ) object, producing an overall increase in entropy for the system.

Another way of thinking about this is that it is impossible for any process to have, as its sole result, heat transferring energy from a cooler to a hotter object. Heat cannot transfer energy spontaneously from colder to hotter, because the entropy of the overall system would decrease.

Suppose we mix equal masses of water that are originally at two different temperatures, say 20 .0 °C 20 .0 °C and 40 .0 °C 40 .0 °C . The result will be water at an intermediate temperature of 30 .0 °C 30 .0 °C . Three outcomes have resulted: entropy has increased, some energy has become unavailable to do work, and the system has become less orderly. Let us think about each of these results.

First, why has entropy increased? Mixing the two bodies of water has the same effect as the heat transfer of energy from the higher-temperature substance to the lower-temperature substance. The mixing decreases the entropy of the hotter water but increases the entropy of the colder water by a greater amount, producing an overall increase in entropy.

Second, once the two masses of water are mixed, there is no more temperature difference left to drive energy transfer by heat and therefore to do work. The energy is still in the water, but it is now unavailable to do work.

Third, the mixture is less orderly, or to use another term, less structured. Rather than having two masses at different temperatures and with different distributions of molecular speeds, we now have a single mass with a broad distribution of molecular speeds, the average of which yields an intermediate temperature.

These three results—entropy, unavailability of energy, and disorder—not only are related but are, in fact, essentially equivalent. Heat transfer of energy from hot to cold is related to the tendency in nature for systems to become disordered and for less energy to be available for use as work.

Based on this law, what cannot happen? A cold object in contact with a hot one never spontaneously transfers energy by heat to the hot object, getting colder while the hot object gets hotter. Nor does a hot, stationary automobile ever spontaneously cool off and start moving.

Another example is the expansion of a puff of gas introduced into one corner of a vacuum chamber. The gas expands to fill the chamber, but it never regroups on its own in the corner. The random motion of the gas molecules could take them all back to the corner, but this is never observed to happen ( Figure 12.10 ).

We've explained that heat never transfers energy spontaneously from a colder to a hotter object. The key word here is spontaneously . If we do work on a system, it is possible to transfer energy by heat from a colder to hotter object. We'll learn more about this in the next section, covering refrigerators as one of the applications of the laws of thermodynamics.

Sometimes people misunderstand the second law of thermodynamics, thinking that based on this law, it is impossible for entropy to decrease at any particular location. But, it actually is possible for the entropy of one part of the universe to decrease, as long as the total change in entropy of the universe increases. In equation form, we can write this as

Δ S tot = Δ S syst + Δ S envir > 0 . Δ S tot = Δ S syst + Δ S envir > 0 .

Based on this equation, we see that Δ S syst Δ S syst can be negative as long as Δ S envir Δ S envir is positive and greater in magnitude.

How is it possible for the entropy of a system to decrease? Energy transfer is necessary. If you pick up marbles that are scattered about the room and put them into a cup, your work has decreased the entropy of that system. If you gather iron ore from the ground and convert it into steel and build a bridge, your work has decreased the entropy of that system. Energy coming from the sun can decrease the entropy of local systems on Earth—that is, Δ S syst Δ S syst is negative. But the overall entropy of the rest of the universe increases by a greater amount—that is, Δ S envir Δ S envir is positive and greater in magnitude. In the case of the iron ore, although you made the system of the bridge and steel more structured, you did so at the expense of the universe. Altogether, the entropy of the universe is increased by the disorder created by digging up the ore and converting it to steel. Therefore,

and the second law of thermodynamics is not violated.

Every time a plant stores some solar energy in the form of chemical potential energy, or an updraft of warm air lifts a soaring bird, Earth experiences local decreases in entropy as it uses part of the energy transfer from the sun into deep space to do work. There is a large total increase in entropy resulting from this massive energy transfer. A small part of this energy transfer by heat is stored in structured systems on Earth, resulting in much smaller, local decreases in entropy.

[AL] Ask students what would happen if the second law of thermodynamics were not true. What if the direction of flow of energy were not predictable? Would life on Earth be able to function?

Solving Problems Involving the Second Law of Thermodynamics

Entropy is related not only to the unavailability of energy to do work; it is also a measure of disorder. For example, in the case of a melting block of ice, a highly structured and orderly system of water molecules changes into a disorderly liquid, in which molecules have no fixed positions ( Figure 12.11 ). There is a large increase in entropy for this process, as we'll see in the following worked example.

Worked Example

Entropy associated with disorder.

Find the increase in entropy of 1.00 kg of ice that is originally at 0 °C 0 °C and melts to form water at 0 °C 0 °C .

The change in entropy can be calculated from the definition of Δ S Δ S once we find the energy, Q , needed to melt the ice.

The change in entropy is defined as

Here, Q is the heat necessary to melt 1.00 kg of ice and is given by

where m is the mass and L f L f is the latent heat of fusion. L f = 334 kJ/kg L f = 334 kJ/kg for water, so

Because Q is the amount of energy heat adds to the ice, its value is positive, and T is the melting temperature of ice, T = 273 K T = 273 K So the change in entropy is

The change in entropy is positive, because heat transfers energy into the ice to cause the phase change. This is a significant increase in entropy, because it takes place at a relatively low temperature. It is accompanied by an increase in the disorder of the water molecules.

Practice Problems

  • 1.84 × 10 3 J/K
  • 3.67 × 10 3 J/K
  • 1.84 × 10 8 J/K
  • 3.67 × 10 8 J/K

Check Your Understanding

Use these questions to assess student achievement of the section's learning objectives. If students are struggling with a specific objective, these questions will help identify which and direct students to the relevant content.

What is entropy?

  • Entropy is a measure of the potential energy of a system.
  • Entropy is a measure of the net work done by a system.
  • Entropy is a measure of the disorder of a system.
  • Entropy is a measure of the heat transfer of energy into a system.

Which forms of energy can be used to do work?

  • Only work is able to do work.
  • Only heat is able to do work.
  • Only internal energy is able to do work.
  • Heat, work, and internal energy are all able to do work.
  • All the spontaneous processes result in decreased total entropy of a system.
  • All the spontaneous processes result in increased total entropy of a system.
  • All the spontaneous processes result in decreased or constant total entropy of a system.
  • All the spontaneous processes result in increased or constant total entropy of a system.

For heat transferring energy from a high to a low temperature, what usually happens to the entropy of the whole system?

  • It decreases.
  • It must remain constant.
  • The entropy of the system cannot be predicted without specific values for the temperatures.
  • It increases.

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Thermodynamics problems and solutions

thermodynamics problems physics

When solving a Physics problem in general and one of Thermodynamics in particular, it is important to  follow a certain order . Get used to being organized when you solve problems, and you will see how it gives good results. It is worth spending a little time on the previous analysis of a problem before you tackle it.

thermodynamics problems physics

The solved thermodynamic problems shown in these pages make use of these three concepts: work ,  heat and  internal energy to a closed system , generally an ideal gas . These three concepts are related through the First Law of Thermodynamics . We will use the so-called Clausius convention to express the first law: the work is done by the thermodynamic system on its surroundings . In addition, the sign convention that we will use is the following one:

Sign convention : 

  • The work done by a gas on its surroundings is positive when it expands. When the gas compresses, the work is negative.
  • The heat absorbed by a system is positive. The heat supplied by a system to its surroundings is negative.

In addition, we will always use the SI units.

When solving a Thermodynamic problem, follow the following steps:

  • Read carefully the Problem Statement..
  • Draw a picture of the physical situation depicted in the problem statement.
  • Write in your notebook the givens in the problem statement.
  • Identify the equations that you will have to use to solve the problem.
  • Be careful with the signs for the heat, the work and the internal energy variation.
  • Do not forget to include the units in your results.
  • Review the problem and check that the results you have obtained make sense.

Consult the summary table to see how to calculate the work, the heat exchanged and the change in the internal energy for the four main reversible processes of an ideal gas .

On the following pages you will find solved Thermodynamic problems. Try to do them yourself before looking at the resolution.

  • Calculation of the work done by an ideal gas
  • Application of the First Law of Thermodynamics
  • Reversible cycle with an adiabatic process (ideal gas)
  • Theoretical Diesel cycle
  • Theoretical Otto cycle
  • Entropy change of a thermal reservoir and of the universe (Carnot heat engine)
  • Entropy change in irreversible processes - real refrigerator
  • Joule expansion


Book cover

  • © 2023

Exercises in Classical Physics—Mechanics and Thermodynamics

Basics of Theory and Solved Problems

  • Francesco Scotognella 0

Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy

You can also search for this author in PubMed   Google Scholar

Includes topics covered in an experimental physics course

Presents a brief theoretical introduction enriched by demonstrations and insight

Solves many problems clearly and systematically

Part of the book series: Undergraduate Texts in Physics (UNTEPH)

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Table of contents (9 chapters)

Front matter, kinematics of a material point.

Francesco Scotognella

Dynamics of a Material Point

Work and energy, systems of material points, relative motions, fluid mechanics, thermodynamics, back matter.

Experimental physics is an important part of the education of anyone interested in science or engineering, serving as one of the fundamental fields of knowledge for understanding how the world around us functions. This textbook seeks to present the topics usually covered in an experimental physics course for aspiring scientists and engineers in a concise but comprehensive manner. The book is organized into ten chapters on different topics, including work and energy, gravity, relative motions, and fluid mechanics. Proof of the most important theorems is given, and additional information is provided to stimulate the curiosity of the students. At the end of each chapter, performed exercises and exercises with solutions are offered to illustrate the chapter’s points and make their importance even clearer. Based on the author’s teaching notes from his own lectures, this book proves invaluable to anyone with an interest in developing a clearer understanding of such topics as mechanics and thermodynamics.

  • experimental physics undergraduate textbook
  • undergraduate textbook mechanics exercises
  • thermodynamics
  • solved problems in thermodynamics
  • Brief theory basics
  • undergraduate textbook thermodyamics exercises

Francesco Scotognella (b. 1982) is an associate professor in the Physics Department at Politecnico di Milano. He studied at Università di Parma and Università di Milano-Bicocca, where he earned a Ph.D. in Materials Science in 2009. He has been a visiting scientist at the University of Toronto (2008) and Berkeley Labs (2016-2018) and a visiting professor at Nanyang Technological University in Singapore (2013). He is currently studying the optical properties of nanomaterials and nano-heterojunctions. In particular, he is exploring new types of junctions for alternative infrared solar cells. He has taught courses on Fundamental Physics at Politecnico di Milano since 2013, as well as at different schools of Engineering. He also currently teaches a course focused on the optical properties of nanosystems at the Ph.D. School of Physics at Politecnico di Milano.

Book Title : Exercises in Classical Physics—Mechanics and Thermodynamics

Book Subtitle : Basics of Theory and Solved Problems

Authors : Francesco Scotognella

Series Title : Undergraduate Texts in Physics

DOI : https://doi.org/10.1007/978-3-031-35074-0

Publisher : Springer Cham

eBook Packages : Physics and Astronomy , Physics and Astronomy (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

Softcover ISBN : 978-3-031-35076-4 Due: 29 December 2023

eBook ISBN : 978-3-031-35074-0 Published: 27 November 2023

Series ISSN : 2510-411X

Series E-ISSN : 2510-4128

Edition Number : 1

Number of Pages : VII, 110

Number of Illustrations : 27 b/w illustrations, 17 illustrations in colour

Topics : Thermodynamics , Classical Electrodynamics , Classical Mechanics

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College Physics : Thermodynamics

Study concepts, example questions & explanations for college physics, all college physics resources, example questions, example question #1 : college physics.

thermodynamics problems physics

We will make the left side for the steel and the right side for water. Thus:

thermodynamics problems physics

Example Question #1 : Thermodynamics

thermodynamics problems physics

We need to use the equation for thermal expansion in order to solve this problem:

thermodynamics problems physics

We are given:

thermodynamics problems physics

Now we have enough information to solve for the change in the length of steel.

thermodynamics problems physics

  • We must account for two separate processes since the ice is melting and then warming. The basic formula to calculate the change in entropy at a constant temperature when the ice melts is:

thermodynamics problems physics

Now we plug in our known values into the equation:

thermodynamics problems physics

The basic formula to calculate the change in entropy at a changing temperature when the water warms is:

thermodynamics problems physics

next we integrate this equation to get:

thermodynamics problems physics

Next we plug in the values we know and solve for the change in entropy:

thermodynamics problems physics

We add our two entropy values together to find the total change in entropy to be:

thermodynamics problems physics

If an ideal gas has its temperature doubled while its volume is cut in half, what happens to its pressure?

thermodynamics problems physics

There is no change in the pressure

thermodynamics problems physics

In this question, we're told that an ideal gas undergoes a change in its temperature and volume, and we're asked to determine how its pressure changes.

First, we'll need to recall the ideal gas equation.

thermodynamics problems physics

Then, we can rearrange to isolate the term for pressure.

thermodynamics problems physics

 The first step in this question is to convert the mass of oxygen given into moles.

thermodynamics problems physics

Next, it's important to recognize that we'll need to use the ideal gas equation. Since we're told that the gas is under STP (standard temperature and pressure), we have everything we need to solve for volume.

thermodynamics problems physics

What is true regarding the work performed by a system whose volume remains constant and undergoes an increase in pressure?

The surroundings does work on the system

The system does work on its surroundings

The system does no work

The work done by the system increases the temperature of the system

To answer this question, it's important to remember how work is defined when dealing with volume and pressure.

The equation for the work done by a gas on its surrounding is as follows.

thermodynamics problems physics

Suppose that a piston contains a gas which begins at a certain pressure and volume. First, the gas in the piston undergoes an isothermal expansion to triple its initial volume. Next, the gas undergoes an isobaric contraction back to its original volume. Finally, the gas undergoes an isochoric increase in pressure until it has returned to its original pressure. Which of the following is a true statement regarding the work done by this gas?

thermodynamics problems physics

In this question, we're told the process that a gas takes through various changes in conditions. From this information, we're asked to find a true statement regarding the work done by the gas in this process.

thermodynamics problems physics

If we were to show this on a pressure vs. volume curve, it would look like the following.

Cyclic gas process

Remember that any pressure-volume work done by a gas is the area under the curve of a pressure vs. volume diagram. For a cyclic process, as the one in this problem, the work done by the gas will be the area within the above image.

For this problem, we don't need to calculate the exact amount of work done. Instead, we can get a rough estimate by first realizing that the structure shown in the above diagram is close to forming a right triangle, but it is slightly smaller. Thus, if we can use the left and bottom sides of the image above to calculate the area that would be enclosed by a right triangle, we can infer that the work done in this problem will be slightly less than the calculated area.

The area for a triangle is the following.

thermodynamics problems physics

Finally, since this represents the area for a right triangle, we know that the actual work done is less than this. Hence, the correct answer is:

thermodynamics problems physics

We know that with the ideal gas law that:

thermodynamics problems physics

We also know with isothermal processes, that the work done on a gas is:

thermodynamics problems physics

Since the number of moles and the temperature is not given to us in the question, we can make a substitution with the ideal gas law to get:

thermodynamics problems physics

Now we can plug in our known values into the equation to solve for the amount of work energy transferred through the isothermal process.

thermodynamics problems physics

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An Overview of Thermodynamics

The Physics of Heat

  • Thermodynamics
  • Physics Laws, Concepts, and Principles
  • Quantum Physics
  • Important Physicists
  • Cosmology & Astrophysics
  • Weather & Climate

thermodynamics problems physics

  • M.S., Mathematics Education, Indiana University
  • B.A., Physics, Wabash College

Thermodynamics is the field of physics that deals with the relationship between heat and other properties (such as pressure , density , temperature , etc.) in a substance.

Specifically, thermodynamics focuses largely on how a heat transfer is related to various energy changes within a physical system undergoing a thermodynamic process. Such processes usually result in work  being done by the system and are guided by the laws of thermodynamics .

Basic Concepts of Heat Transfer

Broadly speaking, the heat of a material is understood as a representation of the energy contained within the particles of that material. This is known as the kinetic theory of gases , though the concept applies in varying degrees to solids and liquids as well. The heat from the motion of these particles can transfer into nearby particles, and therefore into other parts of the material or other materials, through a variety of means:

  • Thermal Contact is when two substances can affect each other's temperature.
  • Thermal Equilibrium is when two substances in thermal contact no longer transfer heat.
  • Thermal Expansion takes place when a substance expands in volume as it gains heat. Thermal contraction also exists.
  • Conduction is when heat flows through a heated solid.
  • Convection is when heated particles transfer heat to another substance, such as cooking something in boiling water.
  • Radiation is when heat is transferred through electromagnetic waves, such as from the sun.
  • Insulation is when a low-conducting material is used to prevent heat transfer.

Thermodynamic Processes

A system undergoes a thermodynamic process when there is some sort of energetic change within the system, generally associated with changes in pressure, volume, internal energy (i.e. temperature), or any sort of heat transfer.

There are several specific types of thermodynamic processes that have special properties:

  • Adiabatic process - a process with no heat transfer into or out of the system.
  • Isochoric process - a process with no change in volume, in which case the system does no work.
  • Isobaric process - a process with no change in pressure.
  • Isothermal process - a process with no change in temperature.

States of Matter

A state of matter is a description of the type of physical structure that a material substance manifests, with properties that describe how the material holds together (or doesn't). There are five states of matter , though only the first three of them are usually included in the way we think about states of matter:

  • superfluid (such as a Bose-Einstein Condensate )

Many substances can transition between the gas, liquid, and solid phases of matter, while only a few rare substances are known to be able to enter a superfluid state. Plasma is a distinct state of matter, such as lightning 

  • condensation - gas to liquid
  • freezing - liquid to solid
  • melting - solid to liquid
  • sublimation - solid to gas
  • vaporization - liquid or solid to gas

Heat Capacity

The heat capacity, C , of an object is the ratio of change in heat (energy change, Δ Q , where the Greek symbol Delta, Δ, denotes a change in the quantity) to change in temperature (Δ T ).

C = Δ Q / Δ T

The heat capacity of a substance indicates the ease with which a substance heats up. A good thermal conductor would have a low heat capacity , indicating that a small amount of energy causes a large temperature change. A good thermal insulator would have a large heat capacity, indicating that much energy transfer is needed for a temperature change.

Ideal Gas Equations

There are various ideal gas equations which relate temperature ( T 1 ), pressure ( P 1 ), and volume ( V 1 ). These values after a thermodynamic change are indicated by ( T 2 ), ( P 2 ), and ( V 2 ). For a given amount of a substance, n (measured in moles), the following relationships hold:

Boyle's Law ( T is constant): P 1 V 1 = P 2 V 2 Charles/Gay-Lussac Law ( P is constant): V 1 / T 1 = V 2 / T 2 Ideal Gas Law : P 1 V 1 / T 1 = P 2 V 2 / T 2 = nR

R is the ideal gas constant , R = 8.3145 J/mol*K. For a given amount of matter, therefore, nR is constant, which gives the Ideal Gas Law.

  • Laws of Thermodynamics
  • Zeroeth Law of Thermodynamics - Two systems each in thermal equilibrium with a third system are in thermal equilibrium to each other.
  • First Law of Thermodynamics - The change in the energy of a system is the amount of energy added to the system minus the energy spent doing work.
  • Second Law of Thermodynamics - It is impossible for a process to have as its sole result the transfer of heat from a cooler body to a hotter one.
  • Third Law of Thermodynamics - It is impossible to reduce any system to absolute zero in a finite series of operations. This means that a perfectly efficient heat engine cannot be created.

The Second Law & Entropy

The Second Law of Thermodynamics can be restated to talk about entropy , which is a quantitative measurement of the disorder in a system. The change in heat divided by the absolute temperature is the entropy change of the process. Defined this way, the Second Law can be restated as:

In any closed system, the entropy of the system will either remain constant or increase.

By " closed system " it means that every part of the process is included when calculating the entropy of the system.

More About Thermodynamics

In some ways, treating thermodynamics as a distinct discipline of physics is misleading. Thermodynamics touches on virtually every field of physics, from astrophysics to biophysics, because they all deal in some fashion with the change of energy in a system. Without the ability of a system to use energy within the system to do work — the heart of thermodynamics — there would be nothing for physicists to study.

That having been said, there are some fields use thermodynamics in passing as they go about studying other phenomena, while there are a wide range of fields which focus heavily on the thermodynamics situations involved. Here are some of the sub-fields of thermodynamics:

  • Cryophysics / Cryogenics / Low Temperature Physics - the study of physical properties in low temperature situations, far below temperatures experienced on even the coldest regions of the Earth. An example of this is the study of superfluids.
  • Fluid Dynamics / Fluid Mechanics - the study of the physical properties of "fluids," specifically defined in this case to be liquids and gases.
  • High Pressure Physics - the study of physics in extremely high pressure systems, generally related to fluid dynamics.
  • Meteorology / Weather Physics - the physics of the weather, pressure systems in the atmosphere, etc.
  • Plasma Physics - the study of matter in the plasma state.
  • Introduction to Heat Transfer: How Does Heat Transfer?
  • What Is a Thermodynamic Process?
  • What Is an Isothermal Process in Physics?
  • What Is Entropy and How to Calculate It
  • The Isochoric Process
  • What Is Isobaric Process?
  • What Is Conduction?
  • Thermodynamics: Adiabatic Process
  • Calculate the Change in Entropy From Heat of Reaction
  • A Scientific Way to Define Heat Energy
  • The Different Fields of Physics
  • Phases of Matter and Phase Diagrams
  • Laws of Thermodynamics as Related to Biology
  • Specific Heat Capacity in Chemistry
  • Understanding Calorimetry to Measure Heat Transfer

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