❤️ Work formula

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One-way convection of internal energy is a form a transport of energy but is not, as sometimes mistakenly supposed a relic of the caloric theory of heat , transfer of energy as heat, because one-way convection is transfer of matter; nor is it transfer of energy as work.

Nevertheless, if the wall between the system and its surroundings is thick and contains fluid, in the presence of a gravitational field, convective circulation within the wall can be considered as indirectly mediating transfer of energy as heat between the system and its surroundings, though the source and destination of the transferred energy are not in direct contact.

For purposes of theoretical calculations about a thermodynamic system, one can imagine fictive thermodynamic "processes" that occur so slowly that they do not incur friction within or on the surface of system; they can then be regarded to as reversible.

These fictive processes proceed along paths on geometrical surfaces that are described exactly by a characteristic equation of the thermodynamic system.

Those geometrical surface are the loci of possible states of thermodynamic equilibrium for the system. Really possible thermodynamic processes, occurring at practical rates, even when they occur only by adiabatic work, without heat transfer, always incur friction within the system, and so are always irreversible.

The paths of such processes always depart from those characteristic surfaces. Even when they occur only by adiabatic work without heat transfer, such departures always entail entropy production.

In thermodynamics, the quantity of work done by a closed system on its surroundings is defined by factors strictly confined to the interface of the surroundings with the system and to the surroundings of the system, for example, an extended gravitational field in which the system sits, that is to say, to things external to the system.

A main concern of thermodynamics is the properties of materials. Thermodynamic work is defined for the purposes of thermodynamic calculations about bodies of material, known as thermodynamic systems.

Consequently, thermodynamic work is defined in terms of quantities that describe the states of materials, which appear as the usual thermodynamic state variables, such as volume, pressure, temperature, chemical composition, and electric polarization.

For example, to measure the pressure inside a system from outside it, the observer needs the system to have a wall that can move by a measurable amount in response to pressure differences between the interior of the system and the surroundings.

In this sense, part of the definition of a thermodynamic system is the nature of the walls that confine it. A simple example of one of those important kinds is pressure—volume work.

The pressure of concern is that exerted by the surroundings on the surface of the system, and the volume of interest is the negative of the increment of volume gained by the system from the surroundings.

It is usually arranged that the pressure exerted by the surroundings on the surface of the system is well defined and equal to the pressure exerted by the system on the surroundings.

This arrangement for transfer of energy as work can be varied in a particular way that depends on the strictly mechanical nature of pressure—volume work.

The variation consists in letting the coupling between the system and surroundings be through a rigid rod that links pistons of different areas for the system and surroundings.

Then for a given amount of work transferred, the exchange of volumes involves different pressures, inversely with the piston areas, for mechanical equilibrium.

This cannot be done for the transfer of energy as heat because of its non-mechanical nature. Another important kind of work is isochoric work, that is to say work that involves no eventual overall change of volume of the system between the initial and the final states of the process.

Isochoric mechanical work for a body in its own state of internal thermodynamic equilibrium is done only by the surroundings on the body, not by the body on the surroundings, so that the sign of isochoric mechanical work with the physics sign convention is always negative.

When work, for example pressure-volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings.

When mechanical work is done on such an adiabatically enclosed system by the surroundings, it can happen that friction in the surroundings is negligible, for example in the Joule experiment with the falling weight driving paddles that stir the system.

Such work is adiabatic for the surroundings, even though it is associated with friction within the system. Such work may or may not be isochoric for the system, depending on the system and its confining walls.

If it happens to be isochoric for the system and does not eventually change other system state variables such as magnetization , it appears as a heat transfer to the system, and does not appear to be adiabatic for the system.

In the early history of thermodynamics, a positive amount of work done by the system on the surroundings leads to energy being lost from the system.

This historical sign convention has been used in many physics textbooks and is used in the present article. According to the first law of thermodynamics for a closed system, any net change in the internal energy U must be fully accounted for, in terms of heat Q entering the system and work W done by the system: An alternate sign convention is to consider the work performed on the system by its surroundings as positive.

This convention has historically been used in chemistry, but has been adopted in several modern physics textbooks. This equation reflects the fact that the heat transferred and the work done are not properties of the state of the system.

Given only the initial state and the final state of the system, one can only say what the total change in internal energy was, not how much of the energy went out as heat, and how much as work.

This can be summarized by saying that heat and work are not state functions of the system. Pressure—volume work or PV work occurs when the volume V of a system changes.

PV work is an important topic in chemical thermodynamics. As for all kinds of work, in general, PV work is path-dependent and is, therefore, a thermodynamic process function.

In general, the term P dV is not an exact differential. For a reversible adiabatic process, the integral amount of work done during the process depends only on the initial and final states of the process and is the one and the same for every intermediate path.

If the process took a path other than an adiabatic path, the work would be different. In a non-adiabatic process, there are indefinitely many paths between the initial and final states.

This impossibility is consistent with the fact that it does not make sense to refer to the work on a point in the PV diagram; work presupposes a path.

There are several ways of doing mechanical work, each in some way related to a force acting through a distance.

If the force is not constant, the work done is obtained by integrating the differential amount of work,. Energy transmission with a rotating shaft is very common in engineering practice.

Often the torque T applied to the shaft is constant which means that the force F applied is constant. For a specified constant torque, the work done during n revolutions is determined as follows: A force F acting through a moment arm r generates a torque T.

The power transmitted through the shaft is the shaft work done per unit time, which is expressed as. When a force is applied on a spring, and the length of the spring changes by a differential amount dx, the work done is.

Substituting the two equations. Solids are often modeled as linear springs because under the action of a force they contract or elongate, and when the force is lifted, they return to their original lengths, like a spring.

This is true as long as the force is in the elastic range, that is, not large enough to cause permanent or plastic deformation.

Therefore, the equations given for a linear spring can also be used for elastic solid bars. Consider a liquid film such as a soap film suspended on a wire frame.

Some force is required to stretch this film by the movable portion of the wire frame. This force is used to overcome the microscopic forces between molecules at the liquid-air interface.

Therefore, the work associated with the stretching of a film is called surface tension work, and is determined from.

The factor 2 is due to the fact that the film has two surfaces in contact with air. The amount of useful work which may be extracted from a thermodynamic system is determined by the second law of thermodynamics.

Under many practical situations this can be represented by the thermodynamic availability, or Exergy , function. To calculate the serial number of the date before or after a specified number of workdays by using parameters to indicate which and how many days are weekend days, use the WORKDAY.

A date that represents the start date. A positive value for days yields a future date; a negative value yields a past date.

An optional list of one or more dates to exclude from the working calendar, such as state and federal holidays and floating holidays. The list can be either a range of cells that contain the dates or an array constant of the serial numbers that represent the dates.

Dates should be entered by using the DATE function, or as results of other formulas or functions. Problems can occur if dates are entered as text.

It can change the direction of motion but never change the speed. This scalar product of force and velocity is known as instantaneous power.

Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus , the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application.

Work is the result of a force on a point that follows a curve X , with a velocity v , at each instant. The sum of these small amounts of work over the trajectory of the point yields the work,.

This integral is computed along the trajectory of the particle, and is therefore said to be path dependent. If the force is always directed along this line, and the magnitude of the force is F , then this integral simplifies to.

If F is constant, in addition to being directed along the line, then the integral simplifies further to. This calculation can be generalized for a constant force that is not directed along the line, followed by the particle.

Thus, no work can be performed by gravity on a planet with a circular orbit this is ideal, as all orbits are slightly elliptical.

Also, no work is done on a body moving circularly at a constant speed while constrained by mechanical force, such as moving at constant speed in a frictionless ideal centrifuge.

Calculating the work as "force times straight path segment" would only apply in the most simple of circumstances, as noted above.

If force is changing, or if the body is moving along a curved path, possibly rotating and not necessarily rigid, then only the path of the application point of the force is relevant for the work done, and only the component of the force parallel to the application point velocity is doing work positive work when in the same direction, and negative when in the opposite direction of the velocity.

And then the most general definition of work can be formulated as follows:. A force couple results from equal and opposite forces, acting on two different points of a rigid body.

The sum resultant of these forces may cancel, but their effect on the body is the couple or torque T. The work of the torque is calculated as.

The sum of these small amounts of work over the trajectory of the rigid body yields the work,. In this case, the work of the torque becomes,.

This result can be understood more simply by considering the torque as arising from a force of constant magnitude F , being applied perpendicularly to a lever arm at a distance r , as shown in the figure.

Notice that only the component of torque in the direction of the angular velocity vector contributes to the work. The scalar product of a force F and the velocity v of its point of application defines the power input to a system at an instant of time.

Therefore, the work done by a force F on an object that travels along a curve C is given by the line integral:. In general this integral requires the path along which the velocity is defined, so the evaluation of work is said to be path dependent.

If the work for an applied force is independent of the path, then the work done by the force, by the gradient theorem , defines a potential function which is evaluated at the start and end of the trajectory of the point of application.

This means that there is a potential function U x , that can be evaluated at the two points x t 1 and x t 2 to obtain the work over any trajectory between these two points.

It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is. The function U x is called the potential energy associated with the applied force.

The force derived from such a potential function is said to be conservative. Examples of forces that have potential energies are gravity and spring forces.

Because the potential U defines a force F at every point x in space, the set of forces is called a force field. The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity V of the body, that is.

In the absence of other forces, gravity results in a constant downward acceleration of every freely moving object. It is convenient to imagine this gravitational force concentrated at the center of mass of the object.

Notice that the work done by gravity depends only on the vertical movement of the object. The presence of friction does not affect the work done on the object by its weight.

Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r t 1 to r t 2 is given by. Use this to simplify the formula for work of gravity to,.

The negative sign follows the convention that work is gained from a loss of potential energy. The velocity is not a factor here.

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