What is the difference between these two works ?

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Some examples in text book 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 any one give some criterion to distinguish these two works ?

Thank you .
 

Answers and Replies

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.
 
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]).
 
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Thank you all.
 

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