Name: energy forms in thermodynamics
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 26 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.10

SC.912.P.10.2

Thermodynamic Potentials

熱力学的ポテンシャルは、システムの状態を熱力学変数の関数として記述する状態関数です。
内部エネルギーは、エントロピーと体積の関数です。温度と圧力は、それぞれ一定の体積とエントロピーでの内部エネルギーの偏差として表すことができます。
エンタルピーは、システムの内部エネルギーと、その圧力と体積の積の合計に等しくなります。dUを微分して代入すると、エントロピーと圧力の関数としてエンタルピーが減少します。したがって、温度と体積はエンタルピーの偏微分として得られます。
ヘルムホルツ自由エネルギーは、内部エネルギーから温度とシステムのエントロピーの積を差し引いたものとして与えられます。微小な変化の場合、方程式は体積と温度の関数になります。したがって、エントロピーと圧力は、ヘルムホルツ自由エネルギーの偏微分を使用して決定されます。
内部エネルギーをエンタルピーに置き換えると、ヘルムホルツ自由エネルギーがギブス自由エネルギーに変換されます。微分して単純化すると、方程式は温度と圧力の関数にさらに還元されます。同様の計算では、エントロピーと体積をギブスの自由エネルギーの偏微分として表します。

<ol>
	<li>ブランデル、SJおよびブランデル、KM(2010)。熱物理学の概念。第2版。米国ニューヨーク:オックスフォード大学出版局。</li>
	<li>レックス、A(2017)。フィンの熱物理学。第3版。フロリダ州ボカラトン:CRC Press. pp. 163.</li>
</ol>

熱力学的ポテンシャル

熱力学ポテンシャルは、熱力学系の解析に非常に役立つ状態関数です。 彼らにはエネルギーの次元があります。 4 つの重要な熱力学的ポテンシャルは、内部エネルギー、エンタルピー、ヘルムホルツ自由エネルギー、およびギブズ自由エネルギーです。 これらの熱力学的ポテンシャルは、圧力、体積、温度、エントロピーの変数のうち 2 つを使用して表現できます。 これら 2 つの変数は、他の 2 つの変数に対する熱力学的ポテンシャルの変化率として表されます。

内部エネルギーは分子の寄与に基づいています。 系内の位置エネルギーと運動エネルギー。 それはエントロピーと体積の関数です。 したがって、他の 2 つの変数、つまり温度と圧力は、それぞれ一定体積での内部エネルギーとエントロピーの偏微分として表すことができます。

エンタルピーは系の熱量を指し、エントロピーと圧力の関数です。 エントロピーと圧力が一定の場合、エンタルピーの変化は系に伝達される熱に等しくなります。 可逆的等圧過程の場合、エンタルピーは系によって吸収される熱を表します。 温度と体積の式は、それぞれエントロピーと圧力に関するエンタルピーの偏導関数から取得できます。

ヘルムホルツの自由エネルギーは「有用な」エネルギーを測定します。 一定の温度と体積で閉じた熱力学系から得られる仕事。 この系は、ヘルムホルツ自由エネルギーが最小値に達するまで、その周囲で動作します。 エントロピーと圧力は、それぞれ温度と圧力に関するヘルムホルツの自由エネルギーの偏導関数として表すことができます。

ギブスの自由エネルギーは、圧力と温度が重要な変数である問題で使用されます。 温度と圧力が一定の場合に熱力学系で行われる最大仕事量を測定します。 エントロピーと体積の式は、それぞれ温度と圧力に関するギブズ自由エネルギーの偏微分によって取得できます。

熱力学ポテンシャルは、熱力学系の解析に非常に役立つ状態関数です。彼らはエネルギーの次元を持っています。4つ...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The First Law of Thermodynamics

熱力学第一法則

KEY TERMS AND CONCEPTS

主要用語と概念

energy forms in thermodynamics

Thermodynamic potentials are energy-based state functions used to analyze a thermodynamic system. They help describe how a system changes under different conditions. The four main thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy.

These potentials can be written using two of the variables pressure, volume, temperature, and entropy. In each case, the rate of change of the potential with respect to the other two variables gives useful information about the system. This makes thermodynamic potentials a practical way to connect energy changes with measurable conditions.

Internal energy comes from the potential and kinetic energy of the molecules inside a system. It is a function of entropy and volume. From internal energy, temperature and pressure can be found using partial derivatives at constant volume and constant entropy, respectively.

Enthalpy describes the heat content of a system. It is a function of entropy and pressure. When entropy and pressure stay constant, the change in enthalpy equals the heat transferred to the system. For a reversible isobaric process, enthalpy shows the heat absorbed by the system. Temperature and volume can also be obtained from the partial derivatives of enthalpy with respect to entropy and pressure.

Helmholtz free energy measures the useful work from a closed thermodynamic system at constant temperature and volume. The system does work on its surroundings until this free energy reaches a minimum. Entropy and pressure can be written as partial derivatives of Helmholtz free energy with respect to temperature and pressure.

Gibbs free energy is useful when pressure and temperature are the key variables. It gives the maximum work done in a thermodynamic system when temperature and pressure are constant. Entropy and volume can be found from the partial derivatives of Gibbs free energy with respect to temperature and pressure.

Energy Forms in Thermodynamics

thermodynamic systems

Open, Closed, and Isolated Systems

A thermodynamic system is the part of the world that scientists study for its heat and energy behavior. It sits inside a surrounding environment, or surroundings. The system and the surroundings can exchange heat and do work across the boundary that separates them. The immediate surroundings affect the system most strongly because they interact with it directly. A kettle of boiling tea shows how this works in everyday life. The tea and the kettle together form the system. If the lid is open,...

work done during volume change

Gas Work in a Piston Cylinder

Gas work in a piston cylinder describes how pressure and volume change are related in thermodynamics. In mechanics, work happens when a force moves an object. In thermodynamics, work done on a system can be estimated when the system changes volume during a process. A gas can be trapped in a cylinder with a movable piston at one end. When the gas expands from volume V1 to volume V2, it pushes on the piston and moves it by a small distance dr. If the pressure on the piston face is p and the...

path between thermodynamics states

Path Dependence in Gas Work

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same. Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this...

heat and free expansion

Two Gas Paths to the Same Volume

Heat added to a thermodynamic system can lead to the same final state through different paths. The path matters because work and heat depend not only on the initial and final states, but also on the steps in between. In this topic, an ideal gas is used to show two different ways to reach the same volume. In the first case, the gas is in a cylinder with a piston and is heated at a constant temperature. As the gas molecules absorb energy, the gas expands slowly in a controlled isothermal process.

internal energy

How Internal Energy Changes in Gas Systems

Internal energy is the energy stored inside a thermodynamic system. It is the sum of the kinetic and potential energies of the molecules or other particles in the system. Molecular kinetic energy includes translational motion, rotation, and vibration. Molecular potential energy comes from interactions between molecules. A system’s location and overall motion do not affect its internal energy. For an ideal monatomic gas, each particle is a single atom. That means there is no rotational or...

first law of thermodynamics

Heat, Work, and Internal Energy

Heat, work, and internal energy are linked by the first law of thermodynamics. This law is a generalized form of energy conservation. It explains how energy changes when heat is added to or removed from a system, and when the system does work or has work done on it. The change in internal energy equals the heat transferred into the system minus the work done by the system. Added heat increases internal energy. For that reason, heat is taken as positive when it enters the system and negative...

first law of thermodynamics: problem-solving

first-law-of-thermodynamics-problem-solving

First Law of Thermodynamics: Solving Problems

The first law of thermodynamics links internal energy, heat, and work. It states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. This is a general form of energy conservation, and it can be used for any thermodynamic process. To solve a first-law problem, start by identifying the thermodynamic system. Then list the initial and final states of the process. Next, identify the known and unknown quantities. It is...

cyclic processes and isolated systems

Net Work in a Cyclic Thermodynamic Process

A cyclic thermodynamic process returns a system to its initial state. In a cycle, the change in internal energy is zero. An isolated system is different because it has zero heat exchange and zero work, so its internal energy stays constant. For a non-isolated system, the internal energy change is zero only when the process is cyclic. The first law of thermodynamics relates internal energy, heat transfer, and work. It states that the change in internal energy is the difference between the net...

isothermal processes

Isothermal Expansion and Heat Transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained. Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression. Here, an ideal gas in an isolated cylinder expands...

isochoric and isobaric processes

Constant Volume and Pressure in Thermodynamics

Thermodynamic processes can happen at constant volume or at constant pressure. An isochoric process is a constant-volume process. In this case, the volume does not change, so the work done by the system is zero. The first law of thermodynamics still applies, so any heat added or removed changes the internal energy of the system only. A simple example is heating 1000 g of water from 40 degrees celsius to 70 degrees celsius at constant volume. Because the process is isochoric, no work is done by...

heat capacities of an ideal gas i

Ideal Gas Heat Capacity at Constant Pressure

Heat capacity describes how much heat a substance absorbs for a given change in temperature. It is also called thermal capacity, and its SI unit is J/K. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K, and its SI unit is J/kg·K. The video also explains molar heat capacity. This is the amount of heat added or removed to change the temperature of 1 mole of a substance by 1 K. It can be measured at constant volume or constant pressure, and it is...

heat capacities of an ideal gas ii

Ideal Gas Heat Capacity Differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case. At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at...

heat capacities of an ideal gas iii

Ideal Gas Heat Capacity and Degrees of Freedom

Ideal gas heat capacity depends on degrees of freedom, which are the independent ways a gas molecule can move, rotate, and vibrate. If d is the number of degrees of freedom, the molar heat capacity at constant volume can be written in terms of d. The molar heat capacity at constant pressure can also be written using the relationship between the two heat capacities. The ratio of molar heat capacity at constant pressure to molar heat capacity at constant volume is called the ratio of heat...

adiabatic processes for an ideal gas

Gas Temperature Changes in Adiabatic Processes

Adiabatic processes change the temperature of an ideal gas without heat transfer. In an adiabatic compression, no heat is added, but work is done on the gas. That work raises the gas temperature. In an adiabatic expansion, the gas does work and its temperature drops. A common example is the compression of a gas-air mixture inside a car engine cylinder. The compression happens so quickly that there is no time for heat to move between the mixture and its surroundings. Even so, the work done on...

pressure and volume in an adiabatic process

pressure-and-volume-in-an-adiabatic-process

Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

work done in an adiabatic process

Adiabatic Compression in an Engine Cylinder

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3. The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real...

thermodynamic potentials

Thermodynamic potentials are energy-based state functions used to analyze a thermodynamic system. They help describe how a system changes under different conditions. The four main thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These potentials can be written using two of the variables pressure, volume, temperature, and entropy. In each case, the rate of change of the potential with respect to the other two variables gives useful...

maxwell's thermodynamic relations

Using Maxwell's Relations in Thermodynamics

Maxwell's thermodynamic relations help solve problems in thermodynamics. They connect partial differentials for quantities that are hard to measure in the lab with quantities that are easier to measure. This makes them useful for working with temperature, pressure, volume, and entropy. These relations come from thermodynamic potentials and the symmetry of second derivatives. Thermodynamic potentials are exact differentials, so the order of second differentiation does not change the result.

joule-thomson effect

Gas Cooling and Heating in Throttling

Gas cooling and heating in throttling is explained by the Joule-Thomson effect, also called the Joule-Kelvin effect. It describes how a fluid changes temperature when it passes through a valve or porous plug in a thermally insulated system. This type of flow is called a throttling process. In the experiment, a high-pressure gas is forced through a throttle valve or porous plug into a lower-pressure region. The gas expands as it moves into the larger volume. Work is done on the gas as it is...

key terms and concepts

Explore the four thermodynamic potentials—internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy—and how they relate to heat, work, and state variables.

Energy Forms in Thermodynamics | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

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SC.912.P.10.1

Thermodynamic Systems

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Work Done During Volume Change

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Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

In the first process for path A to ...

Heat and Free Expansion

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First Law Of Thermodynamics: Problem-Solving

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Isothermal Processes

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Isochoric and Isobaric Processes

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Work Done in an Adiabatic Process

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Maxwell's Thermodynamic Relations

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SC.912.P.10.3

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SC.912.P.10.5

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SC.912.P.10.6

A. Energy is involved in all physical and chemical processes. It is conserved, and can be transformed from one form to another and into work. At the atomic and nuclear levels energy is not continuous but exists in discrete amounts. Energy and mass are related through Einstein's equation E=mc2.

B. The properties of atomic nuclei are responsible for energy-related phenomena such as radioactivity, fission and fusion.

C. Changes in entropy and energy that accompany chemical reactions influence reaction paths. Chemical reactions result in the release or absorption of energy.

D. The theory of electromagnetism explains that electricity and magnetism are closely related. Electric charges are the source of electric fields. Moving charges generate magnetic fields.

E. Waves are the propagation of a disturbance. They transport energy and momentum but do not transport matter.

Energy Forms in Thermodynamics

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