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I just started learning about thermodynamics in an introductory physics class and am confused about the meaning of 'work' as it has been used thus far.

When I was taught mechanics, my teacher said that work is first and foremost a change in energy ($W= \Delta E$), and you can find the work done using the equation $W = Fcos( \theta)d$.

Furthermore, it seems as though the first law of thermodynamics, $\Delta U = Q + W$, is a direct contradiction to the former principle because one is able to have no work done ($W=0$), and still have a change in internal energy (via heat (Q)). For example, in isometric processes work done is always 0 because work is defined as $W=-P \Delta V$ and change in volume is 0; however, internal energy can still change in isometric processes through heat lost or gain. Wouldn't it be correct to say that work has been done at this point, because the energy of the system has changed (via heat)?

It seems that I have defined something wrong, so my question is what is it? Does work somehow not refer to thermal energy/heat, or does internal energy mean more than just energy? Or is it just a convention in thermodynamics to use 'work' to specifically refer to $W = -P \Delta V$, and NOT to change in energy in general (like it excludes thermal energy transfer)?

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    $\begingroup$ The work defined by $W=\int F*dr$ is mechanical work. In some ways, the 1st law of thermodynamics can be thought of as generalizing the idea that $W=\Delta E$. This generalization is needed because some kinds of energy, like heat, cannot be used to perform work. $\endgroup$
    – PrawwarP
    Dec 4, 2020 at 21:32
  • $\begingroup$ Thank you for the answer! Just to clarify, would it be correct to say that adding heat changes the internal energy, but is not considered mechanical work (since heat cannot perform mechanical work)? $\endgroup$
    – mche1962
    Dec 4, 2020 at 21:44
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    $\begingroup$ If I understand you correctly, yes. $\endgroup$
    – PrawwarP
    Dec 4, 2020 at 21:50
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    $\begingroup$ Internal energy is a physical characteristic (physical property) of the material comprising a system, rather than something you do to the system. Work and heat are forms of energy in transit that you apply to a system to change the internal energy of the material comprising the system. $\endgroup$ Dec 4, 2020 at 21:58

2 Answers 2

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When I was taught mechanics, my teacher said that work is first and foremost a change in energy ($W= \Delta E$), and you can find the work done using the equation $W = Fcos( \theta)d$.

That is correct. This is the means of energy transfer that is generally considered in Newtonian mechanics. But there are actually two types of energy transfer: Work and Heat. Both are covered in thermodynamics. Heat is energy transfer due solely to a temperature difference.

Furthermore, it seems as though the first law of thermodynamics, $\Delta U = Q + W$, is a direct contradiction to the former principle because one is able to have no work done ($W=0$), and still have a change in internal energy (via heat (Q)).

There is no contradiction. That is because in thermodynamics the internal energy $U$ of something is the sum of the kinetic and potential energies of a substance at the microscopic level. This form of energy is not usually covered in mechanics. It deals with the kinetic and potential energies of objects as a whole, i.e., at the macroscopic level.

For example, in isometric processes work done is always 0 because work is defined as $W=-P \Delta V$ and change in volume is 0; however, internal energy can still change in isometric processes through heat lost or gain. Wouldn't it be correct to say that work has been done at this point, because the energy of the system has changed (via heat)?

The internal microscopic kinetic and/or potential energies can be increased or decreased as a result of energy transfer by work and/or heat. The temperature of a substance is a measure of the kinetic energies of the molecules and atoms of a substance. Temperature can be changed by means of heat transfer or work transfer. For example, the temperature of a gas can be increased by doing work on the gas, i.e. by compressing it. The exact same increase in temperature can be caused by heat transfer, i.e., exposing the gas to something at a higher temperature. The end result (increase in temperature) is the same, one due to work the other due to heat.

It seems that I have defined something wrong, so my question is what is it? Does work somehow not refer to thermal energy/heat, or does internal energy mean more than just energy? Or is it just a convention in thermodynamics to use 'work' to specifically refer to $W = -P > \Delta V$, and NOT to change in energy in general (like it excludes thermal energy transfer)?

I'm having a trouble following this. But the point is in thermodynamics that the internal energy (microscopic kinetic and potential energies of the molecules and atoms) can be changed by work and/or heat, and for this reason both work and heat are included in the first law.

In mechanics the kinetic energy of an object as a whole can generally only change as a result of work. Let's take a baseball. I can give it kinetic energy by doing work on it, i.e., by throwing it. But if the ball is sitting on a table and I heated it, it will not acquire a velocity (kinetic energy) as a whole. But the heat will increase the velocities of the atoms and molecules of the ball resulting in a temperature increase. Its internal energy increases.

Thanks, your answer helped me a lot with these concepts. For clarification, is it correct to say: 1.Work can be defined at ALL levels as W=Fd (or something similar)

It is essentially correct to say that work can be defined at all levels as force times displacement, though this product can take several forms. In the case of boundary work (the work done in expanding or contracting the boundaries of a closed system), pressure times volume replace force times displacement. In the case of shaft work for an open system (e.g.,work done by turbines) torque times angular displacement replaces force times displacement. But even these variations still boil down to force times displacement when applicable substitutions are made.

2.Just in mechanics, Work can also be defined as W= change in energy, and this is exclusive to mechanics because in mechanics

Work is the transfer of energy. The consequences of the transfer can be a decrease or increase in the energy possessed by the object between which the energy is transferred.

When your teacher said $$W=\Delta E$$ he/she may have been referring to the work energy theorem, which states that the net work done on an object equals its change in kinetic energy. The key term is net work because work can be positive or negative. Work is positive if the force is in the same direction as the displacement ($θ=0$) and negative if the force is opposite the direction of the displacement ($θ=180^0$). The "change in kinetic energy" refers to the kinetic energy of the object as a whole, i.e., its macroscopic kinetic energy and not the internal microscopic internal energy of the first law, though there is a subtle connection as discussed below.

Work is the only factor that changes energy while in other things like thermo, energy can be changed by other factors other than Work, e.g. Heat

Work is the only factor that can change the macroscopic kinetic or potential energy of objects as a whole, while both work and heat can change the internal microscopic kinetic and/or potential energy of an object.

Hope this helps

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  • $\begingroup$ Thanks, your answer helped me a lot with these concepts. For clarification, is it correct to say: 1.Work can be defined at ALL levels as W=Fd (or something similar) 2.Just in mechanics, Work can also be defined as W= change in energy, and this is exclusive to mechanics because in mechanics Work is the only factor that changes energy while in other things like thermo, energy can be changed by other factors other than Work, e.g. Heat $\endgroup$
    – mche1962
    Dec 5, 2020 at 3:50
  • $\begingroup$ @mche1962 I have updated my answer to respond to your follow up questions. Hope it helps. $\endgroup$
    – Bob D
    Dec 5, 2020 at 15:47
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Work as defined in mechanics deals only with the change in kinetic energy; specifically, translational kinetic energy of the center of mass and rotational energy about the center of mass. It does not deal with changes in internal energy, and does not consider energy transfer from heat.

Work as defined in thermodynamics is a much broader concept and is "energy that crosses a system boundary without mass transfer due to any intensive property difference other than temperature between the system and its surroundings". This work can change the internal energy. The first law of thermodynamics considers work and heat and mass transfer in an overall energy balance for a system.

The confusion is the same name "work" is used to mean two different concepts.

To address this confusion, some have proposed calling the work as defined in mechanics "pseudowork" and using work to only refer to the thermodynamics concept. See DOI:10.1119/1.13173Corpus ID: 123663518 Pseudowork and real work B. Sherwood Published 1983 Physics American Journal of Physics

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