Thread: First Law of Thermodynamics Basic Question

Hi Everyone,

I'm currently studying Physics and am going through common terminology when I stumbled across the First Law of Thermodynamics. The textbook I have states that it can be extpressed as dU = δq + δw, the sum of two path functions/inexact differential.

My questions are:

1) Is my interpretation correct - dU is the differential of the Internal Thermal Energy, δq is the differential of the Heat of the system and δw is the differential of the work undertaken by the system?
2) Why can two path functions contribute to calculate a state function? That is, if my reasoning is correct, why do two factors influenced by the process in which they are produced by, form the basis of the current Internal Thermal Energy of the system. The underlying question I feel is: Why isn't U both a path function?

Cheers

ky.tan1

Originally Posted by ky.tan1

1) Is my interpretation correct - dU is the differential of the Internal Thermal Energy, δq is the differential of the Heat of the system and δw is the differential of the work undertaken by the system?

Yes, it is correct.

Originally Posted by ky.tan1

2) Why can two path functions contribute to calculate a state function? That is, if my reasoning is correct, why do two factors influenced by the process in which they are produced by, form the basis of the current Internal Thermal Energy of the system. The underlying question I feel is: Why isn't U both a path function?

The given internal energy of a system is reached by any combination of heat and work. Path functions depend on the path taken to reach one state from another, whereas a state function is not dependent on the path that was taken.

Thanks Neverfly.

But just to make sure I understand what you're saying, does this make sense? New w depends on the path taken from old w as is the case of Q. However because dU is dependent on dw and dQ, and not on old dU, it is an exact differential or state function?

Originally Posted by ky.tan1

Thanks Neverfly.

But just to make sure I understand what you're saying, does this make sense? New w depends on the path taken from old w as is the case of Q. However because dU is dependent on dw and dQ, and not on old dU, it is an exact differential or state function?

I'm baffled, actually. By two things. One: Why did you ask if it is a state function? I think I'll try this a different way...
Define what a state function is. Given that definition, would a variable that depends on differential heat and work apply to that definition?
Two: Why ask about "old dU?"

I know it's bad form to answer a question with a question, but it's worse form to do homework for another person.

so all your pleasant question is actually an assignment?

Neverfly, I was thinking along similar lines with my second response but couldn't express it in words. A state function which I think I've paraphrased from Wikipedia is a property of a system which is dependent on the current state of the system and not on the method/s in which it acquired its current state.
The reason why I asked if it could be a state function is because I was also confused as to whether it could concurrently be a path function. The text I was consulting stated that it was a state function however, I could not reason as to why two path functions can produce a state function.
However, in response to your question an entity relying on the differential of work and heat, is a state function because the differentials represent the rate of change in work and heat? And therefore by extension it fits the definition of a state function because the differentials of work and heat contribute to the current entity but the differentials do not constitute the methods required to acquire the current state.
As for the reason for asking dU, it is because I don't completely understand the difference between dU = dQ + dw and ΔU = Q + w. Specifically, which situation calls for which formula.
As for answering a question with a question, I don't feel that it is bad form in this case because its thought stimulating. Thanks for the patience.

Merumario, I find your suggestion rather offensive but each to his own. If you assume that a fish can climb a tree,then you'll forever be disappointed. There are still some curious people
in this world.

A bit of chopped and formed product:

Originally Posted by ky.tan1

Merumario, I find your suggestion rather offensive but each to his own. If you assume that a fish can climb a tree,then you'll forever be disappointed. There are still some curious people
in this world.

Actually, he responded to me as I had brought that issue up.
No one here can know whether you're asking for a bit of tutoring or for answers to homework. It's something you kinda have to take with a grain of salt.
In your case, you present the appearance of wanting to understand the topic. But man... there's a lotta people that post a thread asking for the answers, not for help. A lot. Like I said- grain of salt. And no one on the other end can ever really know which it is. Just giving answers is a disservice for two clear reasons:
I could give you an answer and that answer be wrong.
If I gave the correct answer and you didn't know how to reach it, you'll flub the exam.
...ok back on topic...

Originally Posted by ky.tan1

A state function which I think I've paraphrased from Wikipedia is a property of a system which is dependent on the current state of the system and not on the method/s in which it acquired its current state.

Yes, so think of a state function as an integral with an upper and lower limit. It's an initial value or an end result, independent of how that result was achieved. I believe this is what your text or Wikipedia should be claiming.

Originally Posted by ky.tan1

The reason why I asked if it could be a state function is because I was also confused as to whether it could concurrently be a path function.

No. But it makes sense that it's a bit confusing as to what the difference is between the two.
If you have a thermometer, you can measure the temperature of an object- that's its state function, because that state is an end product.
Now, instead of measuring the temperature, what if you measure the heat? This is the difference between heat and temperature; the heat is a path function because the heat put into the object will vary depending on that objects properties. It may take more heat to make one object reach a set state function temperature than another object. This means that heat must be a path function (dependent on objects properties and heat required) whereas temperature is a state function (doesn't matter how you got it there, you got it there!)
Does that help?

Originally Posted by ky.tan1

The text I was consulting stated that it was a state function however, I could not reason as to why two path functions can produce a state function.

See above.

Originally Posted by ky.tan1

However, in response to your question an entity relying on the differential of work and heat, is a state function because the differentials represent the rate of change in work and heat? And therefore by extension it fits the definition of a state function because the differentials of work and heat contribute to the current entity but the differentials do not constitute the methods required to acquire the current state.

Grin

Originally Posted by ky.tan1

As for the reason for asking dU, it is because I don't completely understand the difference between dU = dQ + dw and ΔU = Q + w. Specifically, which situation calls for which formula.

Or... DeltaU=Q-W.

Ah fair enough.

Thanks for the tutoring, it's clarified a lot of misunderstandings about state and path functions. However I have to go through this and read up more

before asking any further questions and avoid being misconstrued as a lazy person who just seeks solutions

Originally Posted by ky.tan1

before asking any further questions and avoid being misconstrued as a lazy person who just seeks solutions

That can be a good thing, yes- but resources can and sometimes must include guidance (Not that I'm a guide, much less a good one.)
In case you missed the tone above- Confidence in your answers is important. You can't fake it and get away with it (And there's no suggestion you had or tried to, rather, I'm pointing out the obvious) but when you're confident in your answers, then you probably have a good working knowledge of the material.
So once you understand something, commit it to confidence. If you've gotten it wrong, whoever the guide is will correct you. But confidence means you won't freeze up on a test or exam and it will help you to understand where you go wrong in future studies when you're confident about what's been established.

So once you understand something, commit it to confidence.

One of the best ways to check how well you're doing is to commit it to writing. Just write down a description of your understanding and see how easily it does or doesn't come to you. (If you need to, pretend you're writing to a nice old retired schoolteacher uncle who takes an interest in the progress of your studies.)

Whenever you feel that you can't express the idea in your own words, go back to your notes or your textbook and see if you really understand that portion.

I like to provide another system which can use inexact differentials. Consider the volume of a fresh clay trumpet shaped vase. The volume can be changed by either adding height dv(height) = c dh, were c is the top cross-selection, or by changing the lower cross-sections of the vase as it is currently existing, changing the shape v(shape). v(shape) = integral(0 to h) dc dh. Which method you use first will alter the amount of any of the two methods you have to use. V(height) and V(shape) are path dependant. but v is a state function.