# First principle of thermodynamics vs classical mechanics

please I need clarification about the first principle of thermodynamics, it's general statement is:

$$\Delta U + \Delta \text{KE} + \Delta \text{PE}= W + Q .$$

Supposing that: $$ΔU = 0$$ and $$Q = 0$$, then: $$\Delta \text{KE} + \Delta \text{PE}= W$$ (of total forces).

But, We know from classical mechanics that :$$\Delta \text{KE} + \Delta \text{PE}= W$$(of non conservative forces)

We get : $$W$$(of non conservative forces)$$= W$$(of total forces)

WHICH IS ABSURD!

• I've removed a number of comments that were attempting to answer the question and/or responses to them. Please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. – David Z Jun 1 '20 at 19:26

## 1 Answer

Nothing is absurd here.

When writing $$\Delta U+\Delta \text{KE} +\Delta \text{PE}=W+Q$$ the work term $$W$$ is work done by non-conservative forces as well as work done by any external conservative forces you haven't included in $$\Delta \text{PE}$$. This is also true in your "classical mechanics" expression $$\Delta \text{KE}+\Delta \text{PE}=W$$

The $$W$$ here is not "net work done by all forces". This is only the case in your "classical mechanics" sense using the work energy theorem of $$W_\text{net}=\Delta \text{KE}$$. Where now you are talking about the work done by all forces.

So, really you have "W(of non conservative forces)= W(of non conservative forces)" which, of course, is fine.