What is the difference between these two works ?

In summary, the conversation discusses the confusion between two types of work - mechanical work in the work-energy theorem and thermodynamic work in the first law of thermodynamics. Although they have similar equations, they differ in terms of assumptions and scenarios. The conversation also mentions the overall energy balance equation and provides a simple example to differentiate the two types of work.
  • #1
variation
39
0
Some examples in textbook make me confused when these two works are discussed at the same time.

One of the works is the (mechanical) work in work-energy theorem:

[tex]
\Delta K = \sum_iW_i,
[/tex]

where [tex]K[/tex] is the kinetic energy and [tex]W_i[/tex] was the work done by the [tex]i[/tex]-th force.

The other is the (thermodynamical) work in the first law of thermodynamics:

[tex]
\Delta U = Q + W,
[/tex]

where [tex]U[/tex] is the internal energy of the system, [tex]Q[/tex] is the heat transfered, and [tex]W[/tex] is the work done on the system by surroundings.

Are the two works the same when we want to use work-energy theorem and the first law of thermodynamics at the same time?

Can anyone give some criterion to distinguish these two works ?

Thank you .
 
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  • #2
Hi Variation:

You might want to refer to the overall energy balance equation:

dPE + dKE + dU = Q - W

Now the first equation have certain assumptions, that the change in potential energy is zero (such as it is on a flat surface) and the change in internal energy is zero (no state changes, or temperature and pressure changes). This is your classic pulling a block on a flat surface problem.

The second equation, you have thermodynamic work. You have state changes, and this assumes that no mechanical energy, potential energy or kinetic energy. So basically on a flat surface and not moving. A classic problem is the cylinder with the piston. You put it near the flame and it would expand. Flame provides heat (Q) and expansion is work (W)

I hope this helps.
 
  • #3
This two works are barely the same. Let me give you the simplest example. Internal energy is
[tex] U = U(S, V, N) [/tex]
with
[tex] dU = TdS - PdV + \sum \mu dN [/tex]
[tex] -PdV = dW [/tex]
being the elementary mechanical work.
You get precisely the same elementary work with mechanics of continuous media (consider the simplest case of a diagonal stress tensor [tex] \sigma_{ij} = -P \delta_{ij} [/tex]).
 
  • #5
Thank you all.
 

FAQ: What is the difference between these two works ?

What is the difference between these two works?

The difference between these two works can vary depending on the specific works being compared. However, some common differences may include the time period in which the works were created, the medium or format in which they were created, the subject matter or themes explored, and the intended audience or purpose of the works.

How do the styles of these two works differ?

The styles of these two works can differ in many ways. Some possible differences may include the use of color, composition, technique, or perspective. The style of a work can also be influenced by the cultural, historical, or artistic movements of the time period in which it was created.

What are the similarities between these two works?

The similarities between these two works can also vary depending on the works being compared. However, some common similarities may include the use of similar subject matter or themes, similar techniques or styles, or similar cultural or historical influences. There may also be similarities in the artist's intentions or messages conveyed through the works.

In what ways do these two works differ in their impact or significance?

The impact or significance of these two works can differ in many ways. Some possible differences may include the level of influence the works have had on art, culture, or society, the critical reception or acclaim of the works, or the lasting legacy or relevance of the works in contemporary times.

How can the context in which these two works were created affect their differences?

The context in which these two works were created can play a significant role in their differences. The cultural, historical, political, and social climate of the time period can influence an artist's style, subject matter, and intentions. Additionally, the audience or purpose for which the works were created can also impact their differences.

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