Name: how internal energy changes in gas systems
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 29 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

Energy

PHYS.PS3.7

Internal Energy

시스템의 내부 에너지는 시스템에 있는 모든 개별 원자의 운동 에너지와 위치 에너지의 합으로 정의할 수 있습니다.
단원자 이상 기체 시스템을 생각해 보십시오. 가스가 일정한 부피로 가열되면 원자의 운동 에너지가 증가하지만 원자 사이에 상호 작용이 없기 때문에 위치 에너지는 0으로 유지됩니다.
따라서 내부 에너지는 단원자 원자의 평균 운동 에너지에 의존합니다. 2개의 NkBT에 대해 3으로 표현되며, 여기서 N은 기체 원자의 수, kB는 볼츠만 상수, T는 온도입니다. 따라서 일정한 부피에서 이상 기체의 내부 에너지는 온도에만 의존합니다.
시스템의 내부 에너지는 상태 함수입니다. 실온으로 냉각된 끓는 물은 얼음을 실온으로 녹여 얻은 물과 동일한 내부 에너지를 가지고 있습니다.
따라서 내부 에너지는 시스템의 상태에만 의존하며, 그것을 얻기 위해 사용된 경로에 의존하지 않습니다. 따라서 경로 독립적입니다.

<ol>
	<li>Young, H.D. 및 Freedman, RA (2012). 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : 피어슨. 629쪽.</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전] pp. 115–116. 원본 주소 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy">https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy</a></li>
</ol>

내부 에너지

열역학 시스템의 내부 에너지는 시스템에 있는 모든 분자 또는 실체의 운동 에너지와 위치 에너지의 합입니다. 개별 분자의 운동 에너지에는 회전 및 진동으로 인한 기여와 병진 에너지가 포함됩니다. 위치 에너지는 시스템의 한 분자와 다른 분자 사이의 상호 작용에만 관련됩니다. 내부 에너지에 관한 한 시스템의 위치나 모션은 아무런 영향을 미치지 않습니다.

이상적인 단원자 기체를 생각해 보세요. 여기서 각 분자는 단일 원자입니다. 결과적으로 회전 또는 진동 운동 에너지가 없습니다. 또한 원자간 상호작용이 없으므로 위치에너지는 0으로 가정됩니다. 따라서 내부 에너지는 병진 운동 에너지의 결과입니다. 따라서 이상기체의 내부에너지는 분자수에 분자당 평균 운동에너지를 곱한 값입니다. 따라서 n몰의 이상 단원자 기체에 대한 내부 에너지는 다음과 같이 주어진다.

<img alt="Equation1" src="/files/ftp_upload/13678/13678_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

이상단원자 기체의 주어진 양의 내부 에너지는 온도에 따라 달라지며 기체의 압력 및 부피와 무관하다는 것을 알 수 있습니다. 다른 시스템의 경우 내부 에너지는 그렇게 간단하게 표현될 수 없습니다. 그러나 내부 에너지의 증가는 종종 온도의 증가와 연관될 수 있습니다.

일반적으로 열량 Q이 시스템에 추가되고 시스템이 과정 중에 작업을 수행하지 않으면 내부 에너지는 Q만큼 증가합니다. 엠>. 시스템이 주변 환경에 대해 팽창하여 W 작동하고 과정 중에 열이 추가되지 않으면 에너지가 시스템을 떠나고 내부 에너지가 감소합니다. Q와 W는 경로에 의존하는 반면, 열역학 과정 중 시스템의 내부 에너지 변화는 초기 및 최종 상태에만 의존하고 다음 경로에 의존하지 않습니다. 서로.

열역학 시스템의 내부 에너지는 시스템에 있는 모든 분자 또는 개체의 운동 에너지와 위치 에너지의 합입니다. 운동 ...

Education

교육

JoVE Core

물리학

Unit 1

제1단원

The First Law of Thermodynamics

열역학 제1법칙

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 vibrational kinetic energy. There are also no interatomic interactions, so the potential energy is taken as zero.

In that case, the internal energy comes only from translational kinetic energy. So the internal energy of an ideal gas depends on the number of molecules and the average kinetic energy per molecule. For n moles of an ideal monatomic gas, the internal energy is set by temperature. It does not depend on the gas pressure or volume.

For other systems, internal energy is not so easy to write in a simple form. Even so, a rise in internal energy is often linked to a rise in temperature. When heat Q is added to a system and the system does no work, the internal energy increases by the same amount. When a system does work W by expanding against its surroundings and no heat is added, energy leaves the system and the internal energy decreases.

Heat Q and work W depend on the path taken during the process. The change in internal energy does not. It depends only on the initial and final states of the system.

How Internal Energy Changes in Gas Systems

how-internal-energy-changes-in-gas-systems

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

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

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...

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 how internal energy depends on molecular motion, temperature, heat, and work in ideal monatomic gases and other thermodynamic systems.

How Internal Energy Changes in Gas Systems | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Physical Science

HS-PS3-4

Arizona Science Standards

HS.P4

HS.P4U1.8

HS+Phy.P4

HS+Phy.P4U1.6

Florida Department of Education

SC.912.P.10

SC.912.P.10.2

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS3-3

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

Types of Potential Energy

Potential energy is also known as energy at rest or stored energy. Common types of potential energy include the gravitational potential energy stored in ...

Types of Kinetic Energy

The amount of kinetic energy of an object depends on its mass and speed. Consider two balls of different masses rolling down an inclined plane at the same ...

Kinetic Energy - I

It&#8217;s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the ...

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Elastic Potential Energy

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is ...

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

/files/media/science-education/science-education-thumbs/14702.jpg

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature ...

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the ...

conduction-convection-and-radiation-problem-solving

Conduction, Convection and Radiation: Problem Solving

There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting ...

Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. Identify and calculate different types of energy and their transformations (thermal, kinetic, potential, including magnetic and electrical potential energies) from one form to another in a system. EXPLANATION:  In 6.PS3 students were introduced to the various types of energy and mechanisms for their transformations. Students should now be able to quantify the total energy of a system as well as quantify each different type of energy in a system. Energy is an abstract concept that does not have a physical form. It is a substance-like quantity that is recognized to be conserved as a system changes. Calculations present an opportunity to observe that potential energies are due to the positions of objects within a field, while kinetic energy is based on an object’s mass and motion. Students can evaluate the total energy of a system by imagining that there are different types of energy storage accounts, just as money can be stored in different accounts. Energy can transferred into or out of any of these accounts. Three different processes can account for all energy changes: working, heating, and radiating. In energy storage due to field effects, such as gravitational or electrostatic fields, the field itself stores the potential energy and not the object in the field.

PHYS.PS3.1

What is Energy?

The universe is composed of matter in different forms, and all forms of matter contain energy. &#xA0;The different forms of energy on Earth originate from ...

Heat Flow and Specific Heat

Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of ...

Investigate conduction, convection, and radiation as a mechanism for the transfer of thermal energy.Investigate conduction, convection, and radiation as a mechanism for the transfer of thermal energy. EXPLANATION: Thermal energy is the energy of a system due to the motion of the particles in that system. One object can transfer its thermal energy to another object through the processes of heating or radiating. Convection and conduction are processes which require a physical medium to transfer the thermal energy. In the case of conduction, two objects are in direct contact, while convection transfers thermal energy through a liquid or gaseous medium. Radiation is a unique form of energy transfer which can transfer without a medium. One packet of this energy is called a photon. The energy of the photon determines the effect that it will have when it interacts with matter. Low energy photons such a microwaves add to the motion of matter and result in an increase of the thermal energy. Photons carry energy from the sun to Earth.

PHYS.PS3.2

Quantifying Heat

Thermal Energy&#160;

Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a ...

Free-falling Bodies: Introduction

All objects, neglecting air resistance, fall with the same acceleration towards the Earth&#39;s center due to the force exerted by the Earth&#39;s ...

Free-falling Bodies: Example

An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the ...

force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular ...

force-and-potential-energy-in-three-dimensions

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function ...

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the ...

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         Use the principle of energy conservation and mathematical representations to quantify the change in energy of one component of a system when the energy that flows in and out of the system and the change in energy of the other components is known.         EXPLANATION:  In PHYS.PS3.1 students quantify the various types of energy and consider methods for energy transfer. If a student is able to evaluate the total energy of a system, such evaluations before and after a change to a system provide a mechanism to show that energy of a system has been conserved. For example, students might use pie charts to show the distribution of the total energy. For an object about to freefall, the pie chart might be 100% gravitational potential energy. Mid-descent, the energy might be half gravitational potential energy and half kinetic energy. After colliding with the ground, the total energy may have decreased, which can be represented as heat energy lost from the pie chart.

PHYS.PS3.3

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

Impulse

According to Newton&#8217;s second law of motion, the rate of change of the momentum of an object is the net external force acting on it. The total change ...

Impulse-Momentum Theorem

The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called ...

Conservation of Momentum: Introduction

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its ...

Conservation of Momentum: Problem Solving

Solving problems using the conservation of momentum requires four basic steps:

	Identify a closed system, where the total mass is constant, and no net ...

Types Of Collisions - I

When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a ...

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the ...

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the ...

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions ...

collisions-in-multiple-dimensions-introduction

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each ...

collisions-in-multiple-dimensions-problem-solving

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should ...

Assess the validity of the law of conservation of linear momentum (p=mV) by planning and constructing a controlled scientific investigation involving two objects moving in one dimension. Assess the validity of the law of conservation of linear momentum (p=mV) by planning and constructing a controlled scientific investigation involving two objects moving in one dimension. EXPLANATION: Momentum is a useful tool when considering conservation of energy when two objects interact. Attempts to quantify all energy transformation in such a system often fail to account for energies lost due to the production of sound and heat. Collisions where energy is dissipated from the system are known as inelastic collisions. Though system energy may be lost to the surroundings, the conservation of momentum will still be observed. Thus the conservation of momentum can provide a tool to evaluate inelastic collisions.

PHYS.PS3.4

Temperature and Thermal Equilibrium

Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as ...

Heat Capacity: Problem-Solving

The heat capacity of a gas is the amount of heat energy required to raise the temperature of a unit mass of gas by one degree Celsius. It is an important ...

Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system. Construct an argument based on qualitative and quantitative evidence that relates the change in temperature of a substance to its mass and heat energy added or removed from a system.  EXPLANATION: Two different materials will undergo different degrees of temperature change even with the same amount of energy added to each. Heat capacity is a ratio (the slope of a temperature vs. heat added) that describes the change in temperature of a sample dependent on the amount of heating. Empirical determination of the heat capacity of a substance requires that both phase and mass of the substance are constants. Students can utilize proportional reasoning in the design of a second portion of this experiment to determine the effect of mass on temperature change.

PHYS.PS3.5

Work-energy Theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared ...

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work-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

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Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use.  Define power and solve problems involving the rate of energy production or consumption (P=∆E/∆t). Explain and predict changes in power consumption based on changes in energy demand or elapsed time. Investigate power consumption and power production systems in common use. EXPLANATION:  This standard pairs well with PHYS.PS3.6. Students should understand that a given task will require a certain minimum amount of energy. In accordance with the work-energy theorem, this would be described as work done on the system. Power incorporates a rate element into this discussion. An object can be lifted to an identical height by two different mechanisms. The total energy input into the system (the object and Earth’s gravitational field) will be the same in either case. However, if one mechanism for lifting the object does this in a smaller amount of time, it is said to be more powerful. Students may compare two different devices that accomplish the same task, but have different power ratings and explain the impact of the different power ratings on how the devices are used. For example, two microwaves might both pop a bag of popcorn, but a more powerful microwave might do it faster or be more likely to burn the popcorn at recommended time settings.

PHYS.PS3.6

How Internal Energy Changes in Gas Systems

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