The first law of thermodynamics

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Hi everyone

I'll keep this short and simple, for the formula for the first law of thermodynamics how come the formula can be either negative or positive? E.G ΔU= Q + W/ ΔU = Q - W

Punctuation error.
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Hi everyone

I'll keep this short and simple, for the formula for the first law of thermodynamics how come the formula can be either negative or positive? E.G ΔU= Q + W/ ΔU = Q - W

Yes this confuses many people and is not the only situation in Science where sign conventions differ.

Here we have the situation that the original Laws of Thermodynamics were written by folks who worked with steam engines.

They put coal or wood into the machine and took mechanical work out.

To derive the First Law break the process down into two stages, so there is an intermediate stage.
First add the heat put in from the coal, then subtract the work performed by the machine.

The machine must have had some internal energy to start with add to this the heat energy  from combustion of the fuel and you get the intermediate total internal energy as a sum

${U_{{\mathop{\rm int}} ermediate}} = {U_0} + Q$

Then we get the machine to perform some work - that is we extract work.
This must come from the internal energy, which is now increased to Uintermediate

${U_{final}} = {U_{start}} + Q - W$

Which means that we subtract the work

$\Delta U = {U_{final}} - {U_{start}} = Q - W$

Which is the form you will find today in most engineering and many Physics texts.

But if you look carefully you will note that the heat added is input and the work extracted or output.

When other scientists started to widen thes scope of these laws they wanted to consider all forms of energy, not just heat and work.

Furthermore they wanted them all to be additive (that is you could put work in as well as take it out etc)

So they adopted the sign convention that all forms of energy are considered positive in themselves, and it is the input or output that carries the sign.

So input is positive and output is negative for all forms of energy.

This leads to the form of the First Law used by Chemists

$\Delta U = Q + W$

Where Qis the heat added to the system and W is the work done on the system,

So if heat is generated by the system or work done by the system they are negative.

Edited by studiot
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Nice historical perspective.
Thanks Studiot.

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Thanks for the incredibly informative response. I'm starting to understand the formula, however I have some questions that I gotta ask.

From the formula  (ΔU= Q+W) are you claiming that Q and W can be negative? Furthermore when "heat is generated" via work done or from the heat added to the system, surely the values of Q and W would be positive instead of negative right?

Observing the formula further, I don't understand why W can be a positive when it needs to derive energy from Q in order for work to be done.

ΔU=Q+W

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Thanks for the incredibly informative response. I'm starting to understand the formula, however I have some questions that I gotta ask.

From the formula  (ΔU= Q+W) are you claiming that Q and W can be negative? Furthermore when "heat is generated" via work done or from the heat added to the system, surely the values of Q and W would be positive instead of negative right?

Observing the formula further, I don't understand why W can be a positive when it needs to derive energy from Q in order for work to be done.

ΔU=Q+W

(and the negative sign in the other formula refers to the operation of subtraction).

All quantities involved in that summation have a positive or negative sign as well.

I say summation because the modern First Law includes other forms of energy as well

So    ΔU=Q+W  + gravitational potential energy + electrical energy + ............+.......

Each of these can be positve or negative quantites in their own right so imagine the confusion if you had to remember a formula where some where added and some subtracted.

Since it is possible to have a a single sign convention which applies to all quantities, it is so much easier.

Not all summations are so fortunate.

Why on earth should  Q and W  not be either positive or negative.
This was one of Joule's earliest experiments, to heat water with a mechanical paddle.

From the formula  (ΔU= Q+W) are you claiming that Q and W can be negative? Furthermore when "heat is generated" via work done or from the heat added to the system, surely the values of Q and W would be positive instead of negative right?

Say you have an electric fire.

You have electric energy in and heating effect out

Now say you have an electric motor

You have electric energy in and work out.

Now say you have a dynamo

You have work in and electric energy out

Now say you have a steam turbine electric generator.

You have heat in and electric energy out.

Note the First Law is really a restricted form of the Law of Conservation of Energy and it is desirable for all forms to be set out the same.

Another form is Bernoulli's equation in Fluid Mechanics which considers conservation of

Gravitational enrgy + pressure enrgy + kinetic energy of the fluid.

Edited by studiot
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On 10/8/2020 at 2:49 PM, studiot said:

Here we have the situation that the original Laws of Thermodynamics were written by folks who worked with steam engines.

[...]

Nice historical account. Thank you.

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